The Big Bang | Berean Archive

"Big Bang cosmology is not a single theory but 5 separate theories constructed on top of one another… Thus the Dark Energy floor could crumble leaving the rest of the building intact. But if the Expansion floor collapsed then the entire edifice above it would founder." — Michael Disney, Cardiff University, 2007¹

"Quite amazingly, the baryon density that is inferred from the seven measures of D/H agrees with the baryon density derived from the cosmic microwave background at one percent precision!" — Ryan Cooke, who made the deuterium measurement, 2024²

"The BAO theory assumes standard physics, including the general theory of relativity. That is an extrapolation from the tests in the solar system and smaller… to the scales of cosmology. Would you be inclined to trust an extrapolation of fifteen orders of magnitude?" — Jim Peebles, Nobel Lecture, 2019³

Summary

"The Big Bang" is not one theory. It is a stack of six claims that can be held separately, built up over a century, and several members of the family have been falsified while the family name stayed the same. Almost every argument in this subject goes wrong by attacking the wrong layer.

Three layers are very strongly supported, and a Christian who rejects them is fighting on bad ground.

Expansion. Four independent tests — supernova time dilation, the microwave background's temperature at high redshift, cluster velocities measured by scattering, and the reciprocity theorem — separate expansion from the alternatives. Danny Faulkner, a young-earth astronomer, argues in a young-earth journal that "denial of the expansion of the universe interpretation of the Hubble relation amounts to a denial of general relativity."⁴
The light elements. Standard big bang nucleosynthesis has exactly one adjustable number, and that number is now measured twice by unrelated physics. Deuterium in quasar absorbers gives a baryon density of 0.02227 ± 0.00043; the microwave background's acoustic peaks give 0.02230 ± 0.00021. They differ by 0.13 percent.⁵
The microwave background. A blackbody good to fifty parts per million, which no superposition of ordinary sources can produce.⁶ Lensed by intervening mass at 43σ.⁷ And ten thousand galaxy clusters have been discovered by looking for the shadow they cast in it.⁸

Three layers are much weaker, and this is where the real arguments are.

Inflation cannot be falsified by any finite measurement, because one surviving family of models pushes its signature arbitrarily close to zero.⁹ Paul Steinhardt, who helped build it, calls the paradigm "fundamentally untestable, and hence scientifically meaningless."¹⁰
Dark matter is measured but not detected. The Bullet Cluster shows unseen mass at 8σ using nothing but general relativity.¹¹ Forty years of direct searches have found nothing and have now reached the irreducible neutrino background.¹²
The cosmological constant is the worst quantitative failure in physics — theory exceeds observation "by some 120 orders of magnitude," in Steven Weinberg's words.¹³

And four things are simply unsolved.

Lithium-7 is over-predicted by a factor of 3.3, at 4.4σ, and twenty years of work have not fixed it.¹⁴
The matter-antimatter asymmetry has no accepted explanation. The Standard Model's CP violation is about ten orders of magnitude too small, and the electroweak transition is a smooth crossover rather than the boiling the mechanism requires.¹⁵ ¹⁶
The initial state was extraordinarily special, and Roger Penrose's objection to inflation as an explanation has never been answered: smoothing processes use the Second Law, they do not explain it.¹⁷
The Hubble constant disagrees with itself by nine percent, at 4.5 to 7σ, and the disagreement has grown as measurements improved.¹⁸

Several popular arguments against the Big Bang are dead, and some were retracted by the creationists who made them. The missing Sunyaev-Zel'dovich shadow (withdrawn by John Hartnett in print), redshift quantisation (killed by Hartnett's own analysis), the absence of microwave-background lensing (rebutted in a footnote in 2006 and buried by measurement since), gigaparsec structures, the lithium-6 problem, and the "not enough ionizing photons" objection — which JWST solved in the course of producing the early-galaxy results that get cited as a problem.

One creationist argument is right, and this article concedes it. The claim that the 25-percent helium abundance was retrofitted has real historical merit: the famous 1948 Alpher-Bethe-Gamow paper predicted no helium number at all, the predicted value drifted from 0.36 to 0.25 over thirteen years, and the microwave background's temperature was never successfully predicted — the published values ran from 3 K to 50 K.

And the theology runs the opposite way from the folklore. The theory was published by a Catholic priest who refused to identify it with Genesis and who objected when a pope tried to. It was named by an atheist who spent his life trying to refute it, and who called a beginning "an irrational process that cannot be described in scientific terms." A later pope warned Christians against "making uncritical and overhasty use for apologetic purposes" of it.

The stack, and what each layer costs

Layer	Claim	How strong	If it fell
1. Expansion	Distances between galaxies grow with time	Very strong — four independent tests	Everything above falls
2. Hot early phase	The universe was once denser and above a billion kelvin	Very strong — light-element abundances	Layers 3-6 fall
3. Microwave background	A relic blackbody from when atoms formed	Very strong — spectrum, lensing, scattering, acoustic peaks	Layers 4-6 fall
4. Structure formation	Gravity grew tiny ripples into galaxies	Strong; details unresolved	Layers 5-6 fall
5. Dark matter	Most matter is invisible, cold, and not atoms	Strong that it exists; no detection of what it is	Layer 4 needs replacing; 1-3 survive
6. Inflation, dark energy	Early acceleration; late acceleration	Weakest. Inflation barely testable; Λ unexplained	Layers 1-4 untouched

The detachability of the top two layers is not this article's invention. Barnes and Lewis, who work in the field, say it outright: the darkness of the night sky, the redshift-distance relation, supernova time dilation, galaxy dimming, the microwave background's blackbody spectrum and its temperature-redshift scaling, the Lyman-alpha forest and the light elements "do not depend on the amount of dark matter and dark energy."¹⁹ They add what cosmologists actually think of the dark sector: "cosmologists would dump the dark components in a moment. If someone convinced us that the universe could be explained convincingly – without raising even bigger problems – using only ordinary matter, we would gleefully throw all our dark matter and dark energy models in the garbage bin."¹⁹

What this article covers, and what it does not

It covers the model itself: what the various Big Bang models are, which parts are well supported, which are not, and which arguments against it work.

Competing cosmologies get their own treatment. The static-space Doppler model is worked through in detail in The Doppler Model of Galaxy Redshifts. Young-universe cosmologies, distant starlight, and the dark-matter alternatives are separate articles. Fine-tuning is treated in Is the Universe Fine-Tuned for Life?, and this article follows the choice made there: Penrose's number is used qualitatively and never as a probability.

Every source is catalogued with what it measured and which way it cuts in a companion page: the literature.

Part 1 — "The Big Bang" is not one model

Ask ten people what the Big Bang theory says and you will get ten answers. That is not carelessness. The phrase names a family of models built up in layers over a century, and several members of the family have been falsified while the family name stayed the same.

A century of models, in order

Year	Model	What it actually claimed	Status now
1917	Einstein static universe	Closed, matter-filled, held still by a cosmological constant	Dead — unstable, and the universe expands
1917	de Sitter	Expanding but empty; redshifts from geometry alone	Dead as a description of our universe
1922, 1924	Friedmann	Time-varying solutions of Einstein's equations for a uniform universe. Pure mathematics — no data, no physics of the early state²⁰	Correct; still the backbone of every model below
1927	Lemaître	Expanding solution plus the velocity-distance law plus a numerical expansion rate, from real data. No beginning — it expands out of an Einstein static state in the infinite past²¹	Superseded, but this is the first real Big Bang cosmology
1929	Hubble	Empirical velocity-distance relation, 500 km/s/Mpc. No model attached²²	Relation confirmed; his rate was 7× too large
1931	Lemaître's "primeval atom"	The universe began as a single quantum that decayed. Not hot, not a singularity — a nucleus-density object the size of the solar system²⁰	Dead in detail; ancestor of every "the universe had a beginning" model
1932	Einstein-de Sitter	Flat, matter-only, no cosmological constant²³	Falsified, after sixty years as the textbook "standard Big Bang"
1948	Gamow, Alpher & Herman	Hot Big Bang: elements built in a hot dense early phase, leftover blackbody radiation predicted	Alive. This, not Lemaître's, is the ancestor of the modern model
1948	Bondi & Gold; Hoyle	Steady state: no beginning, matter created continuously²⁴	Falsified — radio source counts, then the microwave background and helium
1962-65	Zel'dovich cold Big Bang	Same expansion, cold initial state, elements made later	Falsified by the microwave background
1980s	Standard cold dark matter	Flat, matter density = 1, no cosmological constant	Falsified — clustering shape and the age problem
1990-95	ΛCDM	Flat, cosmological constant ≈ 0.7, cold dark matter	The concordance model. Proposed before the 1998 supernovae
1993-	Quasi-steady state	Oscillating, many "little big bangs," no overall beginning²⁵	Effectively dead; no active programme
2000s-	Bouncing, emergent, no-boundary	A Big Bang without an initial singularity	Live minority research programmes
2018	Planck base ΛCDM	Six free parameters, flat, constant Λ²⁶	The current standard
2024-	w₀w_aCDM	Dark energy allowed to change with time²⁷	Live extension, currently contested

Four of these models are falsified, and one of them was the textbook standard for sixty years. If someone tells you the Big Bang has never been wrong, they have not read the history. If someone tells you it has been abandoned, they have not either.

Two details in that table are worth pausing on, because almost every popular account gets them backwards.

Lemaître's 1927 model has no beginning at all. It expands away from an unstable Einstein static state in the infinite past. The beginning arrives four years later, in a one-page letter to Nature.

And the 1931 "primeval atom" is neither hot nor a singularity. Helge Kragh, the historian of the controversy: "there was no initial zero-volume singularity corresponding to an infinite density, but instead everything began in a material proto-universe of a density of the order of an atomic nucleus and a size comparable to the solar system."²⁰ Lemaître never used the phrase "big bang" for anything. His own names were "primeval atom" and "fireworks."²⁰

There is also a piece of history worth recording because it is usually told badly. Lemaître's 1927 paper gives the first published value of what is now called the Hubble constant — 625 km/s per megaparsec — derived from 42 nebulae, two years before Hubble's paper. That derivation is missing from the 1931 English translation, which compresses it to "From a discussion of available data, we adopt R'/R = 0·68 × 10⁻²⁷ cm⁻¹."²⁸ What is also missing is Lemaître's own footnote saying the velocity-distance correlation is "très faible" and that the negative results are "neither for nor against" the relativistic reading of the redshifts.²¹ Lemaître was more candid about the weakness of the 1927 data than the textbooks are.

And Hubble himself never wrote down an expanding-universe model. His preferred interpretation in 1929 was de Sitter's static, empty model, in which part of the redshift is not a velocity at all.²² Before repeating any "even Hubble doubted expansion" line, read Faulkner's Answers Research Journal paper on creationists misquoting Hubble.²⁹

Hot or cold — the split most readers have never heard of

"Big Bang" does not, by itself, say the early universe was hot. Lemaître's was not. The famous 1948 Alpher-Bethe-Gamow paper assumed a cold Big Bang and never mentions thermal radiation.³⁰

The hot version won in 1948 on a physical argument, seventeen years before anyone found the microwave background. Jim Peebles, who later shared a Nobel Prize for this work, states it as cleanly as it can be stated:

The problem with the cold Big Bang picture is that one must postulate some special circumstance that prevents element buildup from happening too early, for otherwise the universe would be left without its most abundant element, hydrogen. The hot Big Bang picture does not have this problem because thermal dissociation by the sea of radiation prevents accumulation of deuterons and their conversion to heavier elements until the temperature has dropped to T_i ≃ 10⁹ K.³⁰

In plain terms: in a cold beginning nothing stops protons and neutrons from sticking together at once, and you burn all the hydrogen. In a hot one the photons keep smashing the deuterons apart until the temperature falls to about a billion kelvin. That thermostat is what produces the observed three-quarters hydrogen, one-quarter helium mixture. The helium abundance is the argument; the microwave background was the confirmation that arrived later.

And the cold model is not a straw man. Anthony Aguirre published a modern version in Physical Review D in 2001, precisely to show that "Big Bang" names a family. Change one number — the ratio of photons to baryons, from about two billion down to about one — and you get a universe with the same expansion and the same geometry but a completely different early history: born already containing carbon and oxygen, with the first stars forming at about a hundred years instead of a hundred million, and no microwave background.³¹

What killed the cold model for our universe is that the microwave background is a direct measurement of that ratio.

This is the clearest illustration of the article's whole thesis: same equations, same expansion, one parameter changed, two completely different universes, and both are Big Bang models.

What killed the steady state

The steady state, proposed by Hermann Bondi, Thomas Gold and Fred Hoyle in 1948, held that the universe looks the same at every epoch and that matter is created continuously. Bondi and Gold's defence of their axiom is worth quoting, because it explains why the theory was so hard to give up:

We do not claim that this principle must be true, but we say that if it does not hold, one's choice of the variability of the physical laws becomes so wide that cosmology is no longer a science.²⁴

Hoyle stated his motive openly, and it was not observational:

This possibility seemed attractive, especially when taken in conjunction with aesthetic objections to the creation of the universe in the remote past. For it is against the spirit of scientific enquiry to regard observable effects as arising from 'causes unknown to science', and this in principle is what creation-in-the-past implies.³²

The earliest decisive result was radio source counts, and it needs no cosmological model at all. In a steady state the universe looks the same at every epoch, so faint — therefore distant, therefore old — radio sources should be no more numerous than the nearby ones predict. Martin Ryle and R. W. Clarke found three times too many in 1961:

the results appear to provide conclusive evidence against the steady-state model.³³

The microwave background finished it in 1965, and the helium abundance closed the last escape.

Four things the model does not say

Most arguments against the Big Bang attack claims the theory does not make.

It is not an explosion in space. An explosion has a centre, an edge, and debris flying outward through pre-existing space. The model has none of those. Every observer everywhere sees the same recession pattern, because the distances between things grow. There is no point you could travel to and find the site of the bang.

It does not say the universe came from nothing. The equations describe a universe that was hotter and denser in the past. Run them backwards far enough and they stop working, which is a statement about the equations.

It does not require a singularity. This surprises people on both sides, and it gets its own section in Part 3.

It is not an atheistic theory. It was published by a Catholic priest, resisted for decades partly because it sounded like creation, and named by an atheist who spent his career trying to refute it. That history is Part 5.

Part 2 — What works

Layer 1: the universe is expanding

This is the foundation. If it goes, everything above it goes. It is also the best-supported claim in the subject.

Distant galaxies' light is shifted to longer wavelengths, and the shift grows with distance. By itself that proves only that something is happening to the light. Three things could do it: the galaxies are moving away through static space, space itself is expanding, or the light loses energy on the way. Four tests separate them.

But first, a constraint that rules out most of the alternatives before the tests even start. The shifts are uniform: every wavelength is stretched by the same factor. The same redshift shows up in 21-centimetre radio waves from hydrogen, in visible lines from sodium and oxygen, and in iron X-ray lines a millionth of a millimetre long — measured with radio dishes, ten-metre optical mirrors and X-ray satellites, and they all agree.

No known material can do that. Luke Barnes and Geraint Lewis give the reason cleanly. To affect light at all, a substance must contain electric charge. But charged parts interact with each other — atoms are bound by electromagnetic forces, and solids are rigid lattices of them. So every real material has a personality: it responds to some wavelengths and ignores others, which is why tinted glass reddens visible light while radio waves pass straight through. A substance that shifted all wavelengths by the same factor would have to be perfectly accommodating, with no internal structure of its own to imprint — and that is exactly what charged matter cannot be.¹⁹

That leaves motion or the geometry of spacetime, both of which shift all wavelengths equally because they act on the light rather than on its interaction with matter. It is a strong constraint, and it does not depend on any cosmological model.

Test 1 — distant events run slow. A supernova at redshift 1 takes twice as long to rise and fall as an identical supernova nearby. This has been measured in supernova light curves, in supernova spectra — the stronger version, since spectral evolution cannot be faked by stretching a light curve — and since 2023 in the variability of 190 quasars monitored for two decades.³⁴ Tired light predicts no such stretching and dies here.

Note carefully what this does not do. A genuine Doppler shift from motion through static space predicts the same stretching. Time dilation kills tired light; it does not distinguish motion from expansion.

Test 2 — the background was hotter in the past. If the microwave background is a relic cooling as the universe expands, its temperature must have been higher earlier, by exactly a factor of (1 + z). This is measurable, because gas clouds along the line of sight to distant quasars are excited by that radiation. Carbon monoxide and neutral carbon absorption give T(z) = (2.725 ± 0.002) × (1 + z)^(1−β) with β = −0.007 ± 0.027 — the predicted scaling, to about 3 percent.³⁵ A water-absorption measurement at redshift 6.34 gives 16.4 to 30.2 K against a predicted 20.0 K.³⁶

This is a serious problem for any static model, and even the standard model's most careful professional critic concedes it. Martín López-Corredoira, whose 2017 review is the most thorough catalogue of the model's problems in print, writes: "the results of Noterdaeme et al. with the exact expected dependence on T = T₀(1 + z) are impressive," and that "one can say with almost total confidence that a local origin of the CMBR in a static Universe is excluded."³⁷

Test 3 — galaxy clusters are at rest in the background. When background photons cross the hot gas of a moving cluster, the scattering shifts the temperature slightly. Measured cluster velocities relative to the background are of order a thousand kilometres per second.³⁸ In a static-space model where redshift is real motion, a cluster at redshift 0.55 would be moving at about 123,000 km/s relative to the background, and the effect would be about thirty-six times larger than what is seen. Clusters are essentially at rest in the microwave background frame, which is what expansion predicts and what real motion forbids.

Test 4 — surface brightness, and this one is misunderstood on both sides. The (1 + z)⁻⁴ dimming of galaxy surface brightness is often claimed as a test that distinguishes expansion from a static Doppler model. It does not. Etherington's reciprocity theorem, proved in 1933, forces the luminosity distance to equal (1 + z)² times the angular-diameter distance in any spacetime with Riemannian geometry, light on null geodesics, and conserved photons — including flat, static, Minkowski space.³⁹ The dimming is a theorem, not a prediction of expansion. What it kills is tired light, which destroys photon energy in transit and is not a metric effect.

And the measurement is messier than either side usually admits. Testing it needs galaxies whose intrinsic surface brightness is known, which means correcting for how stars age and for the wavelength window of the detector. Those corrections are real physics, not fudges — stars do age, and light does redshift out of a camera's range — but they are large. Allan Sandage, who spent a career on this test, closed it out with a verdict that is notably unenthusiastic: "the Tolman test … has not been quite as easily done as I set out … in 1974. It has required many developments not yet made at the time. However, the test seems to have been successful. The Tolman prediction is verified. The expansion would seem to be real."⁴⁰ Barnes and Lewis, who accept the standard model, put the honest summary this way: the Big Bang "survives the surface brightness test. It doesn't fail… But it doesn't pass with flying colours either."¹⁹

This site works through the strongest young-earth alternative — Jason Lisle's static-space Doppler model — in a separate article, and finds that it uses a wrong surface-brightness equation, has a hidden free parameter, and fails against 1,371 published supernova distances. What is worth noting here is the part nobody expects: Lisle agrees in print that his model gives no help with the age of the universe. Asked directly, he answered: "Quite right. The Doppler model is not needed to explain distant starlight in a young universe."⁴¹ In his own model the most distant known galaxy sits 13.85 billion light-years away and its light took 13.85 billion years to arrive.

Layer 2: the light elements

If the universe was once hot and dense, then for a few minutes it was a nuclear reactor. Protons and neutrons could stick together, but nothing heavier than helium could accumulate, because there is no stable nucleus of mass 5 or mass 8. So the reactor should have left hydrogen, a specific amount of helium-4, traces of deuterium and helium-3, and a very small amount of lithium-7 — and then shut down as the universe cooled below about a billion kelvin.

This is big bang nucleosynthesis. It is the most tightly constrained part of the model, and it is where the strongest and the weakest results both live.

The objection: "the theory has a knob"

Standard nucleosynthesis has exactly one adjustable number: the ratio of baryons to photons, written η. Critics have argued for decades that the light-element "predictions" are really fits, because η was tuned until the abundances came out right. The Institute for Creation Research states it plainly: "The Big Bang model has an adjustable parameter, like a tuning knob on a radio, that theoreticians can adjust to ensure that the Big Bang produces the amounts of hydrogen and helium necessary to match observations."⁴²

That objection had real historical merit and this article concedes it. Before about 2003, η was not independently known. Ryan Cooke, who made the modern precision deuterium measurement, calls the 1960s helium result a "postdict" in his own review.² Three further parts of the complaint are also true, and are usually left out of pro-Big-Bang accounts:

The famous 1948 Alpher-Bethe-Gamow paper predicted no helium abundance at all. It is a short letter about a neutron-capture abundance curve, in a cold big bang. Anyone who says "the Big Bang predicted 25 percent helium in 1948" is repeating a myth.
The predicted number drifted. 0.29 to 0.36 in 1953. 0.36 ± 0.04 in 1964 — wrong by more than three of its own error bars.⁴³ 0.26 to 0.28 in 1966.⁴⁴ 0.2477 today.
η itself was uncertain by a factor of three for decades, and Hoyle, Burbidge and Narlikar said so in print.

Now the reply, and it has three parts.

First: helium cannot be tuned, because it barely responds to the knob

The helium fraction scales as η^0.039.⁴⁵ To move the predicted helium fraction by ten percent you would have to change η by a factor of 11.5. To double it, by a factor of about 5.2 × 10⁷.

Meanwhile deuterium goes as η^−1.6 and lithium as η^+2.1. One knob cannot be turned to satisfy four numbers that respond to it with exponents of 0.04, −1.6, −0.58 and +2.1.

This is not a modern rationalization. Jim Peebles demonstrated it in 1966 by varying the assumed density by a factor of twenty-six and finding that helium moved from 0.28 to 0.26.⁴⁴ Helium is set almost entirely by the neutron-to-proton ratio at freeze-out, which depends on the weak interaction rates, the neutron lifetime and the expansion rate — not on the baryon density.

Wagoner, Fowler and Hoyle did not fit η to helium either. In 1967 they lowered it to fix deuterium and helium-3, and then cross-checked the resulting density against Oort's star-count estimate of the mean density of galactic material — a number with no nucleosynthesis in it.⁴⁶ Their answer was about 2 × 10⁻³¹ g/cm³. The modern value is about 4 × 10⁻³¹. A factor of two, from 1967, using a microwave background temperature that had been measured only two years earlier.

And their prediction was framed as a test that could fail — by an author who wanted it to:

The mass fraction of He⁴ produced lies between 0.2 and 0.3 for the universal fireball (assuming T₀ = 3° K), but can be higher in a massive object. It is therefore of great importance to determine helium concentrations in different astronomical bodies. A confirmation of X(He⁴) ≈ 0.4 for B stars and for some planetary nebulae could point toward massive objects as the site of origin for the helium. On the other hand, if it could be shown that X(He⁴) is always close to 0.27, this would be evidence favorable to a universal fireball.⁴⁶

Hoyle was a lifelong steady-state advocate co-authoring the sentence that laid out how his own preferred alternative could win. In 1967 the observations genuinely spanned that range. Retrofitters do not publish falsification criteria for their own alternative.

Second: η is now measured twice, by unrelated physics

The microwave background fixes the baryon density from the relative heights of the acoustic peaks at redshift 1100. That measurement involves no nuclei, no cross sections and no light elements. Deuterium in quasar absorption systems fixes it from nuclear reaction rates measured in accelerators, describing an epoch about 200 seconds after the beginning. That measurement involves no microwave background.

The two answers, as of 2026: Ω_bh² = 0.02230 ± 0.00021 from the microwave background, and 0.02227 ± 0.00043 from twelve deuterium systems. They differ by 0.13 percent.⁵

Cyril Pitrou and colleagues put the parameter counting plainly in a Physics Reports review:

Now that the number of neutrino families and the baryonic densities have been fixed by laboratory measurements or CMB observations, the model has no free parameter and its predictions are rigid.⁴⁷

Brian Fields, Keith Olive and colleagues say the same thing: improved neutron-lifetime measurements, the CMB baryon density, and the LEP measurement of the number of neutrino species "have effectively made BBN a zero-parameter theory."⁴⁵

A fitted parameter has one value by construction. A measured one can disagree with itself, and this one does not.

The honest caveat, and it should not be skipped. A competing and equally defensible treatment of two deuterium-plus-deuterium nuclear cross sections pushes that comparison out to about 2σ, and a 2026 paper proposes new physics during nucleosynthesis to absorb it.⁴⁸ So the fair statement is: agreement somewhere between 0.1 and 2σ, limited by nuclear data, not by cosmology. For scale, the three leading microwave-background experiments disagree among themselves by a comparable amount — 100 Ω_bh² is 2.221 for the South Pole Telescope, 2.238 for Planck and 2.257 for ACT. At this precision everything disagrees with everything by a sigma or two. That is what a frontier looks like, and it is not evidence of a rigged model.

Third — and this is the argument a skeptic cannot get around

If η were being tuned to fit the abundances, there would be no lithium problem. Someone would simply have tuned it away.

The lithium problem exists because η stopped being adjustable in 2003, when WMAP measured it. Cooke says so in as many words: the WMAP result "revealed that the Spite plateau disagreed significantly with the Standard Model value."² A theory with a genuinely free parameter does not produce a 4.4σ failure that its practitioners then spend twenty years unable to fix. It absorbs the discrepancy into the parameter. The persistence of the lithium problem is direct evidence that the parameter is not free.

The scorecard, element by element

Deuterium works, and it carries the argument. Twelve near-pristine quasar-absorption systems give D/H = (2.508 ± 0.029) × 10⁻⁵ with no measurable intrinsic scatter. Cooke's own summary is the best sentence written on the subject for a general reader:

Quite amazingly, the baryon density that is inferred from the seven measures of D/H agrees with the baryon density derived from the cosmic microwave background at one percent precision! The incredible agreement of these two baryon density measures, based on completely independent physics and based on two epochs of the Universe separated by almost 400,000 years, represents a triumph to our cosmological understanding.²

Helium-4 works. The measured primordial mass fraction from fifteen low-metallicity ionised-hydrogen regions is Y_P = 0.2458 ± 0.0013 against a predicted 0.2467 ± 0.0002 — agreement to 0.36 percent. A competing programme gets 0.2402 ± 0.0040, and that systematics dispute is not closed.

Helium-3 is untested, and the article says so. Stars both make and destroy helium-3, the only data come from the solar system and the nearby Milky Way, and the Particle Data Group says outright it is "inappropriate to use ³He (and also D+³He) as a cosmological probe."⁴⁹

Lithium-7 fails, by a factor of 3.3, at 4.4σ. This is a real failure of a real prediction and it should be called one. The nuclear-rate escape route has been closed experimentally. The leading remaining explanation is that the old halo stars we measure destroyed their own lithium. But the one depletion-free measurement, interstellar lithium in the Small Magellanic Cloud, was re-analysed in 2024 and now argues against that explanation. And the new-physics fixes are strangled by deuterium: everything that destroys lithium-7 makes too much deuterium.¹⁴

Fields and colleagues' overall verdict on the four elements is the honest summary:

We see excellent agreement for D/H, good agreement for ⁴He, and strong discrepancy in ⁷Li constitutes the persistent lithium problem.⁴⁵

Planck's own review declines to discuss lithium at all.²⁶

One more thing worth noticing. In 1967 the lithium discrepancy ran the other way — Wagoner, Fowler and Hoyle under-predicted lithium-7 by a factor of about thirty-three.⁴⁶ Today the theory over-predicts it by three. A calculation being bent to fit the data does not change the sign of its own worst error.

And the theory's real inputs, listed honestly. Nucleosynthesis is not input-free. It takes the neutron lifetime (879.4 ± 0.6 s, measured in bottles and beams), about a dozen nuclear cross sections measured in accelerators, Newton's constant, and the number of light neutrino species — 2.9963 ± 0.0074, from the width of the Z boson at LEP. All of those are laboratory measurements. None is a cosmological free parameter. The residual freedom really is one number, and that number is now measured twice.

Layer 3: the microwave background

The sky glows faintly at microwave wavelengths, from every direction, at a temperature of 2.72548 ± 0.00057 K. That number is a weighted mean of fifteen independent measurements — molecular excitation in interstellar clouds, balloons, rockets, South Pole instruments, and satellites.⁵⁰ A thermometer made of cyanogen molecules in a gas cloud and a liquid-helium-cooled satellite radiometer agree to well inside one percent.

Four facts about this glow carry almost all the evidential weight.

It is a blackbody, and an absurdly good one

COBE's FIRAS instrument measured the spectrum across the frequency range 2 to 20 inverse centimetres and found deviations from a perfect Planck curve below 50 parts per million of the peak brightness. The Comptonization parameter is capped at |y| < 1.5 × 10⁻⁵ and the chemical potential at |μ| < 9 × 10⁻⁵.⁶

Why that matters is worth spelling out, because it is the hardest fact for any alternative to explain.

A pile of ordinary sources cannot make a blackbody. Add together blackbodies at different temperatures and the sum is not a blackbody — it is a Planck curve plus a y-distortion. Jens Chluba and Rashid Sunyaev proved this and observed that it is unavoidable: "the superposition of blackbodies with different temperatures in general is not a blackbody."⁵¹ Stars, dust grains, hot gas and hydrogen clouds are all at a spread of temperatures. Their sum leaves a y-distortion, and FIRAS caps y at fifteen parts per million.

And you cannot make a blackbody without making photons. Compton scattering shifts photons in frequency but conserves their number. To build a Planck spectrum you need processes that create photons — double Compton emission and bremsstrahlung — and those only work when the universe is dense and hot. The window closes at a redshift of about 2 × 10⁶, roughly one year after the beginning.⁵² Any large energy injection after that leaves a permanent scar, and FIRAS sees none.

To be fair to the alternatives: there is one surviving proposal for thermalizing starlight in a static universe, using conducting "cosmic needles" of iron dust. Aigen Li's 2003 analysis kills two of the three ways it has been calculated and leaves the third standing but unjustified — it requires needles more than ten thousand times longer than they are wide, filling intergalactic space, with optical physics nobody has validated.⁵³ It is not refuted. It is also not a live research programme, and it still has to beat the superposition theorem and the measured temperature scaling.

It is lensed by intervening mass, and this kills a widely cited argument

In 2005 Richard Lieu and Jonathan Mittaz published a paper titled "On the Absence of Gravitational Lensing of the Cosmic Microwave Background." It is still cited — John Hartnett's flagship anti-Big-Bang article for Creation magazine rests on Lieu — as showing that the background is not behind the galaxy clusters, and therefore not cosmological.

Three things are wrong with that use of it.

First, it is not what the paper claimed. Lieu and Mittaz argued that lensing should smear the angular positions of the acoustic peaks by more than WMAP allowed. Their own conclusion was not that the background is local; it was that something maintains flat geometry over large scales: "the large scale curvature of space may not entirely be an initial value problem related to inflation."⁵⁴ They state no significance level for their central claim anywhere in the paper.

Second, it was rebutted in print within six months, by name, in the standard review of the subject. Antony Lewis and Anthony Challinor's footnote is blunt: "Ref. (37) claims a several-percent effect on the main CMB acoustic peaks; this is incorrect because the scale dependence and correlation of the magnification were not properly accounted for."⁵⁵ The physical reason is that the large magnifications come from structures smaller than an arcminute, and the microwave background is already smooth on those scales because of diffusion damping. Magnifying a smooth patch changes nothing you can see.⁵⁵

Third, measurement then buried it. Lensing of the background is detected at 40σ by Planck⁵⁶ and 43σ by ACT.⁷ The peak smearing that Lieu and Mittaz said was missing is measured precisely enough to be removed: Planck detects the resulting peak sharpening at 15σ, and their lensing paper has a section titled "Acoustic peak sharpening."⁵⁶ Lensing by individual clusters — the case Lieu and Mittaz themselves called the strongest, "because their properties are well understood" — has been detected by three telescopes, in temperature and in polarization alone, and the cluster masses it gives agree with the masses from optical weak lensing and from the cluster gas.⁵⁷

In fairness: in 2005, microwave-background lensing genuinely had not been detected. Theirs was a legitimate challenge that failed. What is not legitimate is citing a 2005 paper in 2026 as though the twenty years since had not happened.

Ten thousand galaxy clusters have been discovered by the shadow they cast in it

When background photons cross the hot gas in a cluster, some scatter off fast electrons and gain energy. The result is a distortion with a fixed spectral shape — a dip below 218 GHz, a rise above it — whose brightness does not fade with distance, because it is a fractional change in a background that is the same everywhere.

The Atacama Cosmology Telescope's 2026 catalogue lists 10,040 clusters found this way, including 1,180 beyond redshift 1 and 124 beyond redshift 1.5.⁸ Planck's all-sky catalogue lists 1,653 detections with 1,203 confirmed.⁵⁸

Read that again. These clusters were found by looking for the shadow, and then confirmed by optical and X-ray telescopes. A background that is not behind the clusters cannot be scattered by their gas, and an artifact cannot be used as a finding chart that keeps turning up real objects.

One caution, because overclaiming here would be easy. The relativistic correction to this effect — a percent-level refinement — is only a 2σ hint, and the one paper that claimed a 5σ detection was withdrawn by its own authors after an error was found in review.⁵⁹ Do not cite that number.

Its ripples have the pattern of sound waves in a hot plasma

Before the universe cooled enough for atoms to form, photons and matter were locked together and pressure waves rang through the mixture. When atoms formed, the ringing froze into a pattern of hot and cold spots with a characteristic angular scale and a series of harmonics.

The peak positions were computed before they were measured. The relative heights of odd and even peaks depend on how much ordinary matter was in the plasma, and that number then matched the deuterium abundance measured in quasar absorption lines, from completely different physics.

The sharpest single check is the phase relationship between temperature and polarization. An adiabatic acoustic mode requires the polarization peaks to land on the temperature troughs. Planck's measured positions: polarization peaks at multipoles 398.3, 690.4, 993.1 and 1296.4; temperature troughs at 416.3, 675.5, 1001.1 and 1290.0.⁶⁰ That is a prediction with no adjustable freedom, and it is checkable by anyone with the two tables side by side.

Was the temperature predicted? No. And conceding that costs nothing

A standard creationist argument runs like this. Arthur Eddington calculated 3.18 K for the temperature of space in 1926, before the Big Bang was proposed. Andrew McKellar measured 2.3 K from interstellar cyanogen in 1941. Meanwhile the Big Bang camp predicted 5 K, then 28 K, then 50 K, and a last-minute 40 K in 1965. So the Big Bang made no successful temperature prediction.

Three of those four factual claims are true, and this article concedes them.

Eddington really did compute 3.18 K, on page 371 of The Internal Constitution of the Stars. But read the next paragraph, on the same page:

Radiation in interstellar space is about as far from thermodynamical equilibrium as it is possible to imagine, and although its density corresponds to 3°·18 it is much richer in high-frequency constituents than equilibrium radiation of that temperature.⁶¹

On the following page he prints a table giving the temperature you would infer from starlight at each wavelength: 690 K at 6000 Å, 967 K at 4000 Å, 1750 K at 2000 Å, 4707 K at 600 Å.⁶¹ Eddington computed what a black-bulb thermometer would warm up to in starlight, and said in the same breath that starlight is not a blackbody. The microwave background is the opposite in every respect — a blackbody to fifty parts per million, with one temperature at every frequency. The two numbers agree by coincidence.

McKellar really did get 2.3 K, and he deserves full credit. Cyanogen's first rotational level sits 3.79 wavenumbers above the ground state, and it is the microwave background that populates it. He was measuring the right thing without knowing what it was.⁶² But he called it the excitation temperature of interstellar cyanogen, said a thermal distribution "must be assumed,"⁶² and doubted whether "the concept of such a temperature in a region with so low a density of both matter and radiation has any meaning."⁶³ He made no cosmological claim.

Worth noting: Fred Hoyle used McKellar's number against the Big Bang in 1950, arguing that Gamow's model would give a temperature "much greater than McKellar's determination."³⁰ That is the exact opposite of the modern creationist use of it.

And the published Big Bang numbers really did wander, badly. 5 K in 1948. 5 K in 1949. 28 K in 1950, because Alpher and Herman adopted a density estimate that turned out to be wrong. Gamow gave 3 K in 1950 with no derivation, 50 K in The Creation of the Universe — by inserting the present age of the universe into a formula that only holds in the radiation-dominated era — then 7 K in 1953 and 6 K in 1956.⁶⁴ The answer is 2.72548 K.

Jim Peebles is blunt about the 1948 number: it "is not significant because it depends on the present baryon density, which was very uncertain, and they compute element buildup along the wrong path."³⁰

Helge Kragh names the deeper failure:

neither Gamow, Alpher, nor Herman suggested that it might actually be detected, and if so, how.⁶⁴

One part of the creationist list is simply wrong. The "40 K prediction" of 1965 was not a prediction. Robert Dicke and colleagues wrote: "Without some knowledge of the density of matter in the primordial fireball we cannot predict the present radiation temperature. However, a rough upper limit is provided by the observation that black-body radiation at a temperature of 40° K provides an energy density of 2 × 10⁻²⁹ gm cm⁻³."⁶⁵ It is an upper limit, in a sentence that begins by saying they cannot predict the temperature.

So where does this leave things?

The temperature was not predicted. Anyone who says "the Big Bang predicted 2.7 K" is overselling, and this article does not say it.

Two working cosmologists say exactly the same thing, and more sharply. Luke Barnes and Geraint Lewis, in a book written to help critics attack the Big Bang properly, state it flatly:

But let's be very clear about one point. The big bang theory does not predict the temperature of the CMB. There is no calculation within the big bang theory that produces the number 2.725 K.¹⁹

Their reason is worth having, because it is structural rather than apologetic: in the model the temperature falls with time, so there is no such thing as "the" predicted temperature. Three billion years ago it was 3.42 K; three billion years hence it will be 2.22 K. What the theory does predict is that radiation coupled to matter in a hot early phase would decouple when atoms formed, at about 3,000 K, and survive as a uniform blackbody at a few kelvin today. They add the honest reason this omission has not cost the model much: "no plausible alternative cosmology has predicted a perfect blackbody spectrum at 2.725 K."¹⁹

And one attribution needs fixing, because this project has repeated the error too. The line often quoted as McKellar's own caution — that the inferred temperature "has, of course, only a very restricted meaning" — is not McKellar's. It is Gerhard Herzberg's, commenting on McKellar's result in his 1950 textbook Molecular Spectra and Molecular Structure.¹⁹ The sentence appears in neither of McKellar's 1941 papers. McKellar's own hedges are the ones quoted above.

But notice what Eddington and McKellar did not predict, and what the hot Big Bang did: a thermal blackbody sea filling all of space, isotropic, decoupled from matter, whose temperature scales as (1 + z), carrying acoustic peaks at calculable angular scales, polarized out of phase with its temperature pattern, and lensed by intervening mass. Every one of those has been measured. Nothing in a static or steady-state universe requires any of them.

Fred Hoyle put the objection in its sharpest form in 1994: "Had observation given 27 kelvins instead of 2.7 kelvins for the temperature, then 27 kelvins would have been entered in the catalogue. Or 0.27 kelvin. Or anything at all."⁶⁶ He is right about the temperature and wrong about everything else. No free parameter in the model produces or spoils a blackbody good to fifty parts per million, and six parameters fix thousands of acoustic bandpowers.

Layer 4: structure, and a ruler laid down before it was measured

The best test in this layer is baryon acoustic oscillations, and it is the clearest case in cosmology of a prediction made first and measured second.

The prediction. Before atoms formed, pressure waves travelled through the photon-baryon plasma. When the photons decoupled, those waves stopped, leaving a preferred separation — the sound horizon — frozen into the distribution of matter. Its length can be computed from the baryon and matter densities, which the microwave background measures. The answer is 147.05 Mpc, determined to 0.2 percent, using no galaxy-survey data at all.²⁷

The measurement. In 2005 Daniel Eisenstein and colleagues found a bump in the clustering of 46,748 luminous red galaxies at exactly that separation:

We find a well-detected peak in the correlation function at 100h⁻¹ Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter.⁶⁷

The significance was 3.4σ, and no microwave-background information was used in the fit.⁶⁷ The 2dF survey found it independently the same year, and their statement of what the result rests on is a model of honest reporting:

What is impressive in our data is not simply that the results suggest departures from a smooth curve, but that these deviations occur in the locations expected from theory. It is this prior knowledge that gives the extra statistical power needed in order to reject a zero-baryon model with confidence.⁶⁸

That cuts both ways, and the article prints it for that reason: the signal is significant because the location was predicted first.

Twenty years later, DESI has measured the same ruler at sub-percent precision in seven independent redshift bins, using over thirty million galaxies and quasars. Same ruler, same predicted length.

A second, weaker confirmation of accelerated expansion. In a universe without dark energy, a photon falling into a growing structure gains exactly the energy it loses climbing out. If the expansion accelerates, the potential well decays while the photon is inside, and the photon comes out slightly hotter. This is the integrated Sachs-Wolfe effect, and it should correlate the microwave background with foreground galaxies.

It has been detected — but honestly, this is a weak result. Twenty years of work with every available survey gives 4 to 4.5σ,⁶⁹ against 8σ for the Bullet Cluster. It confirms accelerated expansion independently of supernovae, which is worth something. It is much weaker than the supernova, microwave-background and acoustic-oscillation evidence, which is worth saying. Planck also reports an anomalously large signal in stacked superclusters and supervoids that "is in conflict with ΛCDM expectations."⁷⁰

One claim in this layer that flipped, and it is instructive

For twenty years a standard objection ran: there are not enough ultraviolet photons from early galaxies to reionize the universe by redshift 6. López-Corredoira's 2017 review states it: "The quasar population is unlikely to provide enough photons to ionize the universe at z ≈ 6."³⁷

JWST measured the ionizing efficiency of ultra-faint galaxies in 2024 and found it four times higher than models had assumed. The authors' conclusion: "the rate of ionizing photons exceeds that needed for reionization, even for escape fractions of order five per cent."⁷¹

The objection is now dead, and the live problem runs the other way. A 2024 paper argues that the galaxies actually observed "not only can drive reionization, but would end it too early," putting the observations in tension with the microwave background's optical depth and with the Lyman-alpha forest.⁷²

Two lessons. First, the same JWST early-galaxy excess that gets cited as a Big Bang problem is what solved this Big Bang problem. Second, the surviving tension is a disagreement about star formation and escape fractions inside an agreed cosmological framework — not a challenge to the framework.

Does anything independent confirm 13.8 billion years?

The age comes out of fitting the microwave background inside the model.²⁶ So the fair question is whether anything checks it from outside. Three clocks do, and none uses a cosmological parameter.

Globular clusters. The oldest star clusters can be dated by where their stars turn off the main sequence — a statement about stellar physics and about the distance to the cluster. A 2021 analysis of 68 clusters gives an age of the universe of 13.5 Gyr, with a statistical error near 0.15 and a systematic error of 0.23 to 0.33.⁷³ A 2023 study that dated M92 by running twenty thousand isochrone sets over every uncertain input gets 13.80 ± 0.75 Gyr, with eighty percent of the error coming from the distance.⁷⁴

White dwarf cooling. A white dwarf is a dead star with no fusion left. It simply radiates stored heat, and the physics of the cooling curve has nothing to do with main-sequence ages. Because the oldest white dwarfs in a cluster have had only a finite time to cool, none is fainter than a certain brightness, and that cutoff is a clock.

In NGC 6752 the cooling clock and the turnoff clock agree: the cooling sequence gives about 14 Gyr, and turnoff fitting gives 13 to 14.⁷⁵ There is also a floor that needs no fitting at all — one halo white dwarf has a cooling age of 10.3 Gyr.⁷⁶

Radioactive dating of individual stars. Thorium-232 and uranium-238 in extremely metal-poor stars decay on 14- and 4.5-billion-year half-lives. Uranium was first detected in a star in 2001, giving 12.5 ± 3 Gyr.⁷⁷

But this third method is much weaker than it looks, and the honest thing is to say so. It needs a theoretical production ratio, and that number is not well known. The same star gives ages five billion years apart depending on which nuclear mass model is used.⁷⁸ Applied broadly, the thorium/europium chronometer has produced ages "from 21 Gyr to −9 Gyr," and about thirty percent of the relevant stars give a negative age.⁷⁹ What this method honestly supports is that the oldest stars are of order ten to fourteen billion years old.

The one to watch. HD 140283, nicknamed Methuselah, has been dated at 14.46, 14.27, 12.01, 12.3, 13.5 and 14.2 billion years by six published analyses since 2013.⁸⁰ ⁸¹ The scatter is not measurement noise; it is which opacity table you build and what mixing length you assume. Note also that even the highest values never exceeded the age of the universe by a statistically significant margin — Bond's own 2013 abstract said the star "does not conflict with the age of the Universe,"⁸² and the 2014 follow-up put the excess at under one standard deviation. The "star older than the universe" story came from press coverage, not from the papers.

The 1990s age crisis — the most instructive episode in the subject

For about five years the standard cosmology of the day was falsified by an age measurement. Both sides should know this story, and both usually tell half of it.

The model then was Einstein-de Sitter, which gives an age of two-thirds of the Hubble time. With the Hubble constant then measured near 80, that is 8.2 billion years. The oldest globular clusters were being dated at 16 ± 3 billion. Lawrence Krauss and Michael Turner in 1995:

The expansion age for a Hubble constant of 80 km s⁻¹ Mpc⁻¹ is 8.2 Gyr for the theoretically favored flat Universe… Therein lies the problem; the ages of the oldest globular clusters are estimated to be 16 ± 3 Gyr… The age problem is more acute than ever before.⁸³

Two things gave way, and neither was a re-observation of the clusters.

The distance scale was wrong. The Hipparcos astrometry mission, plus four other techniques, put globular clusters farther away, which makes their stars intrinsically brighter and therefore younger. Brian Chaboyer and colleagues reported in 1998 that their best estimate had fallen to 11.5 ± 1.3 Gyr — "a systematic shift of over 2σ compared to our earlier estimate, due completely to the new distance scale."⁸⁴ Their own 95 percent lower bound dropped from 12.07 Gyr to 9.5 Gyr.

And the cosmology was wrong. A cosmological constant lengthens the expansion age for the same Hubble constant.

Both readings of this episode are defensible, and giving only one is the mark of a partisan piece.

For the skeptic: for most of a decade the standard model was contradicted by an independent measurement, and it was rescued by revising the independent measurement and by adding a new component. Both fixes came after the problem.

For the standard model, and this is the stronger reading: the Hipparcos revision was an independent astrometric mission, not a cosmological adjustment, and five distance techniques moved together. Dark energy was not invented to fix the age problem — it was independently detected in 1998 by supernova distances, then by the microwave background, then by acoustic oscillations. The same Λ that fixes the ages is the Λ measured three other ways. That is what a healthy theory does under pressure.

And the lesson that must not be skipped: globular cluster ages carry systematic uncertainties large enough to have moved the answer by several billion years once already. Anyone who quotes today's figure as a rock-solid check should be shown the 1995 numbers and asked why this time is different. The honest answer is that Gaia parallaxes are directly measured and far more precise than the 1990s distance ladder, and that modern analyses average over the stellar-physics inputs rather than fixing them. That is a real improvement. It is also an improvement in exactly the quantity that failed before.

The bottom line on ages

No model-independent method is precise enough to confirm 13.797 ± 0.023 billion years. The best has an error bar about fifteen times larger, and the best single-star measurements disagree with each other by two billion years.

What they establish firmly is a floor. There are objects in the Milky Way at least eleven to twelve billion years old on physics that has nothing to do with cosmology, and one white dwarf has been radiating for at least 10.3 billion years on cooling physics alone.

For a young-earth argument that is the decisive fact, and it does not depend on the Big Bang model being right in any detail.

Part 3 — What does not work

Inflation is not yet a testable theory, and its architects say so

Inflation is the proposal that the universe underwent a brief burst of accelerated expansion in its first fraction of a second. Alan Guth proposed it in 1981 to fix three things at once: why space looks flat, why widely separated parts of the sky have the same temperature, and why we see no magnetic monopoles.

Three things should be said in its favour first, because an article that omits them is not honest.

It made a prediction about the density of the universe that could have failed and did not. Inflation drives the average density to the critical value. When it was proposed the measured density was uncertain by a factor of three. Thirty-three physicists, including Guth, Andrei Linde, Stephen Hawking, Steven Weinberg and Edward Witten, made the point in a 2017 letter:

The average mass density of the universe has now been measured to an accuracy of about half of a percent, and it agrees perfectly with the prediction of inflation. (When inflation was first proposed, the average mass density was uncertain by at least a factor of three, so this is an impressive success.)⁸⁵

It predicted a specific small departure from a scale-invariant spectrum of ripples. Planck measures the scalar spectral index as n_s = 0.9649 ± 0.0042 — eight standard deviations from the scale-invariant value of 1, on the side the simplest models require.²⁶

And it predicted correlations larger than the horizon. The anticorrelation between temperature and polarization at large angles is the signature of ripples already in place when a region came into causal contact. But note the hedge the discovery paper itself attached: "In addition to inflation, the pre-Big-Bang scenario and the Ekpyrotic scenario predict the existence of superhorizon fluctuations."⁸⁶ It confirms some epoch of accelerated expansion, not inflation uniquely.

Now the problems.

Inflation is a framework, not a model, and the framework cannot be falsified by any finite measurement. Individual models die regularly. Planck killed φ⁴ and higher monomials in 2013, φ² and natural inflation in 2015, and BICEP/Keck killed φ^(2/3) in 2021. The surviving favourites are Starobinsky's R² model, Higgs inflation and the α-attractors. But α-attractors push the tensor-to-scalar ratio arbitrarily close to zero as one parameter is lowered. No upper limit on that ratio can therefore exclude inflation as such. The current best limit is r_0.05 < 0.036, from BICEP/Keck's 2018 data release, and it has not been improved since.⁹

Inflation regresses to the conditions it was hired to explain. Anna Ijjas, Paul Steinhardt and Abraham Loeb — Steinhardt helped build the theory — put the circularity plainly: "the universally accepted assumption about initial conditions no longer leads to inflation; instead, inflation can only begin to smooth the universe if the universe is unexpectedly smooth to begin with!"⁸⁷ In a popular piece they sharpen it: "if it were easy to find a patch emerging from the big bang that is flat and smooth enough to start inflation, then inflation would not be needed in the first place."⁸⁸

Roger Penrose has the deepest version of this objection, and it is thermodynamic rather than rhetorical. Smoothing is an entropy-increasing process, and any such process presupposes a low-entropy starting point:

All spontaneous symmetry-breaking processes and all phase transitions (these being needed for inflation) take place only by the good grace of the Second Law. These processes do not explain the Second Law: they use it.¹⁷

Penrose is careful and this article will be too: he says his remarks "do not tell us that inflationary cosmology is wrong," only that they undercut the original motivations.¹⁷ Andreas Albrecht, a co-founder of inflation, concedes the point in print: "inflation does not predict the arrow of time. Inflation 'passes the arrow of time buck' to the special initial conditions of the inflaton field."⁸⁹

Guth's own first paper was more modest than anything written about the idea since. Its closing sentence: "I am publishing this paper in the hope that it will highlight the existence of these problems and encourage others to find some way to avoid the undesirable features of the inflationary scenario."⁹⁰

And the flatness "prediction" was defended in whichever direction the data pointed. Linde wrote this in 2014:

Before the discovery of dark energy, many astronomers believed that Ω ~ 0.3. At that time, experts in inflationary theory made many attempts to save inflation by inventing inflationary models compatible with this value of Ω, and none of these models worked except one of two models which were extremely artificial.⁹¹

Those models are real and citable — "An open universe from inflation" and "Inflation with Ω ≠ 1" both appeared in Physical Review D in 1995. A theory whose defenders build a version for whatever the data says is one whose successes have to be discounted.

Steinhardt's strongest wording is the one to quote, because it is his and it is in Nature: "The inflationary paradigm is fundamentally untestable, and hence scientifically meaningless."¹⁰ Guth, David Kaiser and Yasunori Nomura replied, and their reply contains a concession that cuts both ways: "we would view the success or failure of such predictions not as a test of the inflationary paradigm, but rather as part of our exploration of the measure problem."⁹²

One test that would have settled a great deal was cancelled. CMB-S4, designed to reach a sensitivity of σ(r) = 0.0005, lost joint Department of Energy and National Science Foundation support on 9 July 2025. LiteBIRD's goal is r < 0.002.

Dark matter is measured but not detected

Twenty-seven percent of the universe, on the standard accounting, is a substance nobody has caught. That is a real problem. But the evidence that something is there is stronger than critics usually allow, and the two facts have to be held together.

The one piece of evidence that does not depend on cosmology at all is the Bullet Cluster. Two clusters collided. The hot gas — most of the ordinary matter — was slowed and sits in the middle. The gravitational lensing mass, mapped independently from the distortion of background galaxies, sits with the galaxies on either side. Douglas Clowe and colleagues: "An 8σ significance spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law."¹¹ That argument needs only general relativity and a count of the visible baryons.

But notice how little it establishes. It shows mass is unseen in one system. It does not give the universal ratio of dark to ordinary matter, does not show the dark matter is non-baryonic, and does not show it is cold. All three come from the microwave background and from structure formation — inferences inside the model, not independent confirmations of it.

The searches have come up empty, and they are running out of room. The best current limit on a spin-independent WIMP-nucleon cross-section is 2.2 × 10⁻⁴⁸ cm² at 40 GeV.¹² The experiments have now reached the "neutrino fog" — LZ reported 4.5σ evidence of solar boron-8 neutrinos scattering coherently off its xenon, which is the irreducible background that ends this style of search. Roughly a factor of seven of parameter space remains before that floor.

The honest way to put this is Carlos Frenk and Simon White's, and they are two of cold dark matter's principal architects:

even the most ardent supporters of the cold dark matter idea must remain sceptical until the dark matter particles are finally and conclusively discovered.⁹³

A warning about the small-scale problems, because apologetics has not kept up. For twenty years the standard list of dark matter's failures was: too few satellite galaxies, satellites too small, and cores instead of cusps at galaxy centres. Most of that list is closed. On missing satellites: "The 'missing satellites problem', cast in terms of number counts, is thus solved."⁹⁴ A 2022 Nature Astronomy review rates too-big-to-fail solved for satellites and core-cusp "uncertain."⁹⁵

What survives is the diversity of rotation curves — galaxies of the same mass have very different inner rotation curves, and the same pro-ΛCDM review rates that a "strong tension." And the epistemic point survives: the fixes came from tuned baryonic feedback added to the simulations, not from the theory itself.

A second survivor, and it is stronger than most creationist writers realise. The dwarf galaxies orbiting the Milky Way are not scattered at random. Many of them lie in a thin plane, a result first noticed in the 1970s and strengthened as more satellites were found. Andromeda has one too: about half its known dwarfs sit in a plane 36,000 light-years thick and 1.2 million light-years across, and their measured velocities show the plane rotating coherently. Barnes and Lewis, who accept the standard model, are candid about what that means: "This was not predicted by any galaxy formation simulation before it was discovered," and making it work needs the dark matter of those dwarfs guided onto fine planar orbits by filaments that current simulations say are thicker than galaxies — "akin to a gorilla repairing a watch; not impossible, but difficult to imagine."¹⁹ One plane could be a fluke. Two starts to look like something.

The standard replies are that it may still be a statistical accident, or an unmodelled effect of gas physics, or that better astrometry will dissolve it. Those are live possibilities and not dismissals. What matters here is that this is a real, unresolved problem in the layer where dark matter actually does its work.

The cosmological constant is the worst quantitative failure in physics

Dark energy is the name for whatever is making the expansion accelerate. In the standard model it is a constant energy density of empty space.

The problem is that quantum field theory predicts a value for that energy, and the prediction is catastrophically wrong. Steven Weinberg stated it in 1989: "theoretical expectations for the cosmological constant exceed observational limits by some 120 orders of magnitude," and the terms "must cancel to better than 118 decimal places."¹³ Quantum chromodynamics alone, ignoring everything at higher energy, needs 41 orders of cancellation.

This is the largest disagreement between a theoretical prediction and a measurement anywhere in science. Nobody has explained it, and the leading naturalistic proposal — a landscape of vacua with anthropic selection — is an account of how a value might be selected, not of why it takes this one.

Two cautions on how this is often used.

First, the mismatch is not evidence against the Big Bang specifically. The quantum field theory calculation needs no cosmology. The measured value of Λ is a cosmological inference. Reject the standard cosmology and you have not removed the problem; you have removed the number the problem is measured against.

Second, the evidence that Λ is nonzero was weaker at the start than the retelling suggests. Perlmutter's 1999 paper quotes 99 percent confidence — about 2.6σ. Riess's higher figures come with a flatness prior. What made the case was the accumulation of independent probes afterwards.

And it may not be a constant. DESI's second data release prefers evolving dark energy at 2.8σ with Pantheon+ supernovae, 3.8σ with Union3 and 4.2σ with DES-Y5.²⁷ But the Dark Energy Survey walked its own number back in 2026: a recalibration cut 4.2σ to 3.2σ and the authors describe "only a weak preference for evolving dark energy." A 2026 review calls the whole result "a dataset-dependent indication rather than a settled discovery." Watch this one; do not bank on it.

The matter-antimatter asymmetry has no accepted explanation

This is the model's cleanest unsolved problem, and creationist writers use it less than they should.

The fact. There are about 6.12 × 10⁻¹⁰ baryons per photon, and essentially no antimatter — the diffuse gamma-ray background rules out antimatter regions.⁹⁶ So for roughly every billion antiquarks in the early universe there was a billion and one quarks. Everything that exists is the leftover.

Why this is a problem. In 1967 Andrei Sakharov listed three things any explanation must supply: baryon number must not be conserved; the laws must treat matter and antimatter differently; and the universe must depart from thermal equilibrium.⁹⁶

The Standard Model of particle physics supplies the first. It fails the other two, and the failures are not small.

CP violation is about ten orders of magnitude too small. The single CP-violating phase in the quark mixing matrix gives a dimensionless asymmetry measure of about 10⁻²⁰, against the roughly 6 × 10⁻¹⁰ required.¹⁵ An explicit 1994 calculation got a baryon-to-entropy ratio below 1.6 × 10⁻²³ against an observed 4 to 6 × 10⁻¹¹ — a shortfall of about twelve orders of magnitude. Its authors: the effect "is many orders of magnitude below what observation requires, and indicates that non standard physics is indeed needed in the cosmological scenario."⁹⁷

And there is no departure from equilibrium. The electroweak transition would have to be a first-order phase transition — a boiling, with bubbles. Lattice calculations, which are non-perturbative and so not a modelling artifact, show it is first-order only if the Higgs boson is lighter than 72.4 ± 1.7 GeV. That result was published in 1998, before the Higgs was found.¹⁶ The measured Higgs mass is 125.1 GeV. The transition is a smooth crossover,⁹⁸ and Sakharov's third condition is not met.

Note what inflation does here, because it makes the problem worse. Inflation dilutes any pre-existing excess of matter to nothing. So "the universe just started with more matter than antimatter" is not available as an answer inside the standard model. The asymmetry has to be generated afterwards, by physics nobody has found.⁹⁶

The proposals, and their status. Electroweak baryogenesis with new particles is the most testable, and the vanilla version is ruled out. Leptogenesis — CP-violating decays of heavy right-handed neutrinos — works, gets the right order of magnitude, and in its standard form puts the new physics at 10⁸ to 10⁹ GeV, roughly a hundred million times beyond the reach of the Large Hadron Collider.⁹⁶ That is its honest problem: it works and it is essentially untestable.

How much should this count against the Big Bang? Less than it first appears, and this matters for using it honestly. The failure is in particle physics, not in cosmology: the Standard Model is known to be incomplete for independent reasons. What the asymmetry shows is that the first fraction of a second requires physics we do not have.

Jason Lisle presses this argument hard, and his physics is right up to the inference: "if the big bang were true the universe should be 50% matter, and 50% antimatter. But in fact, the universe is essentially 100% matter. Therefore, we must conclude that the big bang is not true."⁹⁹ The step that fails is the last one. The observed asymmetry is not "100 versus 0"; it is one part in a billion surviving annihilation, and that number is measured independently by both the microwave background and nucleosynthesis, and the two agree. The question is why η is not exactly zero, not why it is one.

The singularity, and what the theorems actually prove

This is where both sides go wrong, and it is worth getting exactly right.

The Big Bang model does not require a singularity. The singularity is what you get if you take general relativity, assume it holds all the way down, and extrapolate backwards. Working cosmologists say plainly that this is an extrapolation past where the theory is trusted.

Matt Strassler sorts the model into four confidence zones. From nucleosynthesis onward is green: "we have strong observational evidence that the Hot Big Bang did occur." From there back to a few hundred GeV is yellow — "a highly educated guess … though no direct experimental checks." Inflation's late stages are orange. And before that is red:

So if people tells you that the universe started in such and such a way, perhaps 'with a singularity' or 'with a quantum fluctuation out of nothing' or 'in the Big Crunch (i.e. the collapse) of a previous phase of the universe', remember that they're telling you about the red zone. They're neglecting to tell you that what they're saying is pure theory, with neither an experiment to back it up nor a clear theoretical reason to believe their suggestion is unique and preferable over someone else's alternative.¹⁰⁰

Sean Carroll says the same from the other side of the field: "our current incomplete understanding of quantum gravity is fully compatible with both the possibility that the universe has lasted forever, and that it had a first moment in time."¹⁰¹

The 1965 and 1970 singularity theorems do not apply to the early universe as it is modelled today. Both conclusions are about geodesic incompleteness, not infinite density. And the assumptions fail: a positive cosmological constant has the wrong sign for the theorems, and scalar fields violate the curvature condition outright. José Senovilla and David Garfinkle, in the standard review, state it in one line — "Actually, inflationary cosmological models violate it" — and give the modern reading of what the theorems mean:

A more up-to-date perspective would rather state that they provide very solid evidence of the need of (possibly quantum) corrections to GR when extreme gravity effects occur.¹⁰²

That is a relativist saying, in a peer-reviewed review, that the correct reading of the singularity theorems is "general relativity breaks down here," not "the universe began here."

The 2003 Borde-Guth-Vilenkin theorem is the one apologists use, and it should be quoted exactly. It was written because the older theorems fail. Its abstract:

Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating — or just expanding sufficiently fast — must be incomplete in null and timelike past directions… Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.¹⁰³

Its conclusion, in the authors' own words, is that "some new physics is necessary in order to determine the correct conditions at the boundary."¹⁰³ Not a singularity. Not that physics fails. Not that the universe came from nothing.

Guth, one of the three authors, is explicit about the limits:

There is of course no conclusion that an eternally inflating model must have a unique beginning, and no conclusion that there is an upper bound on the length of all backwards-going geodesics from a given point.¹⁰⁴

Alexander Vilenkin, another of the three, does think it points to a beginning — "The answer to the question, 'Did the universe have a beginning?' is, 'It probably did.' We have no viable models of an eternal universe."¹⁰⁵ He also says this:

Both sides have appealed to the BGV theorem, both sides appealing to me—of all people!—for a better understanding. … But my own view is that the theorem does not tell us anything about the existence of God.¹⁰⁵

An article that quotes only the first half of that is doing to Vilenkin what quote-miners do to us.

There are Big Bang models with no singularity at all. Each of the following keeps the hot dense early phase and the observed expansion, differing only in what replaces t = 0: the ekpyrotic model, where the hot phase comes from a brane collision; the cyclic model, an endless sequence of bangs and crunches; the loop quantum cosmology bounce; the emergent universe, which has "no singularity, no 'beginning of time', and no horizon problem";¹⁰⁶ Hartle and Hawking's no-boundary proposal; Penrose's conformal cyclic cosmology; and eternal inflation.

Some of these are fringe. Some are mainstream. Three of them are still past-incomplete by the BGV theorem. The point is narrower: "the universe had a first moment" is a live scientific question and not a consequence of accepting the Big Bang.

The Hubble tension is real, and it is not what people think

Two ways of measuring today's expansion rate disagree.

Measured from the microwave background, assuming the standard model, Planck gives H₀ = 67.4 ± 0.5 km/s per megaparsec. The South Pole Telescope's 2025 data gives 66.66 ± 0.60 on its own. Measured by climbing a ladder of distance indicators out to distant supernovae, the SH0ES team gets 73.2 ± 0.9, and a 117-author community analysis in 2026 gives 73.50 ± 0.81.¹⁰⁷

The disagreement is variously quoted between 4.5σ and 7.1σ depending on which pair you compare, and it has grown rather than shrunk as measurements improved. That is the signature of a real problem rather than a fluke.

But look at what it is a disagreement about. It is a nine percent disagreement over a calibration. Both numbers give an age near 13 billion years — 13.8 at the low end, 12.8 at the high end. Neither end is remotely compatible with a universe thousands of years old.

Licia Verde, Nils Schöneberg and Héctor Gil-Marín put it in the sentence a reader should carry away:

It appears to be a matter of anchors: the shape of the Universe expansion history agrees with the model, it is the normalizations that disagree.¹⁸

George Efstathiou states the constraint any replacement must satisfy:

If it is argued that new physics beyond ΛCDM is required to explain, for example, distance scale measurements of the Hubble constant (the 'Hubble tension')… then that new physics must reproduce the CMB anisotropies of the base ΛCDM cosmology to extraordinarily high precision.¹⁰⁸

There is also a live dispute inside the distance-ladder camp that outsiders rarely hear about. Wendy Freedman's Carnegie-Chicago programme gets lower numbers — 70.39 from red-giant-branch calibration, 68.81 from JWST data alone — and withdrew its own headline number between 2024 and 2025 after "an issue in the data pipeline and in the photometric reductions of the HST data."¹⁰⁹ The 2026 community consensus paper does not include Freedman, Madore, Jang, Hoyt or Lee, and should not be presented as if the whole field signed it.

Anomalies worth knowing about, at their real significance

The lensing amplitude. Planck's own abstract says "The CMB spectra continue to prefer higher lensing amplitudes than predicted in base-ΛCDM at over 2σ."²⁶ This is an internal inconsistency in the best-measured dataset in cosmology, and Planck flags it themselves. It is not supported by their lensing reconstruction, which is why it did not become a crisis.

The large-angle anomalies. The microwave background has a low quadrupole, an alignment between the quadrupole and octopole nicknamed the "axis of evil," a hemispherical power asymmetry, and a cold spot. Planck's own assessment is the fairest thing written on the subject:

The existence of these features is uncontested, but, given the modest significances at which they deviate from the standard ΛCDM cosmological model, and the a posteriori nature of their detection, the extent to which they provide evidence for a violation of isotropy in the CMB remains unclear. It is plausible that they are indeed simply statistical fluctuations.¹¹⁰

Two of them weakened in 2026 when a larger fraction of the sky was used; the Cold Spot's supervoid explanation died in 2023 when lensing data flipped the odds against it. The hemispherical asymmetry is the one still standing, at roughly 2 to 3σ, and the polarization data do not confirm it.

Nobody should build an argument on any of these. Charles Bennett and colleagues made the point about after-the-fact statistics as well as it can be made, using the microwave sky itself: one of their co-authors noticed that Stephen Hawking's initials appear in the temperature map. "It is certainly infinitesimal; in fact, much less likely than several claimed cosmological anomalies. Yet, we do not take this anomaly seriously because it is silly."¹¹¹

The JWST early galaxies. The 2022 headlines about galaxies too massive to exist did not survive spectroscopy. Ivo Labbé's preprint claimed seven galaxies above 10¹⁰ solar masses; by the time it was published in Nature it claimed six candidates over a narrower redshift range, with the two most extreme masses reduced to one "possible," and the paper says in terms that "all objects in this paper should be considered candidate massive galaxies."¹¹² Every one since observed spectroscopically came in at a lower redshift or a lower mass, and one turned out to be an active galactic nucleus at redshift 5.6 rather than a galaxy at 8.1.

What survives is smaller and more interesting: a quiescent galaxy at redshift 7.3 whose number density exceeds any model by more than a factor of a hundred, and an excess of ultraviolet-bright galaxies at redshift 10 to 14. Those are the live residuals. The "impossible masses" are not.

The strongest professional critic, and how his list has aged

The most serious catalogue of problems with standard cosmology was not written by a creationist. It was written in 2017 by Martín López-Corredoira, a staff astrophysicist at the Instituto de Astrofísica de Canarias, and published in Foundations of Physics: 64 pages, 473 references.

He is worth taking seriously and worth quoting accurately, because popular citations of him routinely drop his hedges:

It is not my purpose to defend a particular theory against the standard cosmology. All theories have their own problems.³⁷

Warning: I review only certain critical papers, and in a few cases I discuss them, but I take no responsibility for their contents… My own position is also neutral, I express no opinion on whether the standard cosmology is correct or not.³⁷

We must also admit that alternative theories are not at present as competitive as the standard model in cosmology in terms of giving better explanations.³⁷

His thesis is "not proven and under-discussed," not "refuted." Nine years on, his list divides sharply.

What he conceded at the time. He scored the temperature-versus-redshift test as a success for expansion, and supernova time dilation too. He called galaxy number counts a draw, and explicitly declined to endorse Lerner's ultraviolet surface-brightness test.³⁷

What has since closed.

He noted that quasars show no time dilation. In 2023 Lewis and Brewer found (1 + z) time dilation in 190 quasars — and cited his paper.³⁴
He asked where the missing baryons were, since less than half the predicted low-redshift baryons had been located. They were found, decisively in 2020, by weighing the entire intergalactic medium using the dispersion of localised fast radio bursts.¹¹³ The total matched the value nucleosynthesis and the microwave background had predicted.
He reported that there were not enough ionizing photons to reionize the universe by redshift 6. JWST found the missing sources.
His Alcock-Paczyński result, which excluded standard ΛCDM at 98 percent confidence using 2017 acoustic-oscillation data, has not been reproduced by DESI's far larger 2025 dataset. A 2σ result that a better dataset does not reproduce is a fluctuation.
On helium he cites, side by side, a 2010 measurement that is too high and a 1992 measurement that is too low. Both cannot be evidence against the same prediction, and neither survived.
On deuterium his entire treatment is one sentence saying the mechanisms are "not properly understood." He wrote it before the one-percent measurement existed.

What is still live, and worth knowing.

The angular-size test is his own research area and his strongest card. Galaxy angular sizes fall roughly as 1/z out to redshift 3 — flat, static, Euclidean behaviour — where the standard model predicts a minimum near redshift 1.6 and a rise beyond it. Reconciling this needs galaxies at redshift 3 to be about six times smaller than galaxies of the same luminosity today.

The honest answer is that the size evolution is measured, not postulated: effective radii at fixed stellar mass do shrink as roughly (1 + z)⁻¹ to (1 + z)^−1.5, in Hubble surveys and now in JWST, and simulations reproduce it. But the sizes were derived assuming the standard model's distances, and the circularity complaint has force. He states the caution himself: "we must be cautious with this interpretation, because of the uncertainty in the galaxy size evolution."³⁷

Eric Lerner's 2018 Monthly Notices paper makes the same case and has never been rebutted in print.

The lithium problem is his other live card, and Part 2 has already conceded it.

Part 4 — The dissident case, and which parts of it survive

The 2004 open letter, twenty-two years on

In May 2004 thirty-four scientists published an open letter in New Scientist attacking Big Bang cosmology. It is still circulating — the Institute for Creation Research quoted it approvingly in 2020 and added "Creation scientists heartily agree." It is the best-known statement of the dissident case, and it deserves a fair hearing before a verdict.

Its opening is its strongest paragraph:

The big bang today relies on a growing number of hypothetical entities, things that we have never observed — inflation, dark matter and dark energy are the most prominent examples. Without them, there would be a fatal contradiction between the observations made by astronomers and the predictions of the big bang theory. In no other field of physics would this continual recourse to new hypothetical objects be accepted as a way of bridging the gap between theory and observation.¹¹⁴

Who signed it matters, in both directions. Two of the three authors of the steady-state theory — Hermann Bondi and Thomas Gold — signed, along with Jayant Narlikar, Hoyle's student and co-author. These are not cranks; Bondi was a Fellow of the Royal Society and Master of Churchill College. But the list is heavily weighted toward the two rival programmes it names — steady state and plasma cosmology — plus Halton Arp's discordant-redshift school, and several signatories are engineers or defence researchers rather than cosmologists. It is the alternative-cosmology community signing its own manifesto, which is what it says it is.

Claim by claim, in 2026:

Claim	Status
Inflation, dark matter and dark energy have never been observed	True, and it is the letter's best sentence. Part 3 concedes it
"Inflation requires a density 20 times larger than that implied by big bang nucleosynthesis"	Confused. Inflation predicts total density ≈ 1; nucleosynthesis constrains the baryon density to ≈ 0.05. That is the dark-matter claim restated, not a contradiction
Without dark energy the universe is only ~8 billion years old, younger than many stars	True as a conditional, and it was a real motivation for Λ. A fair account of why Λ was accepted; a poor argument that it is wrong
"No quantitative predictions that have subsequently been validated"	Dead, and it was already dead in 2004
Plasma cosmology and steady state explain the light elements and the background radiation	Dead. Neither produces a blackbody to FIRAS precision or the acoustic peak positions
Discordant redshift data are "ignored or ridiculed"	Dead. Tested and failed — and the decisive test against redshift quantisation was run by a young-earth creationist
"Doubt and dissent are not tolerated"	Partly live — see below

Sean Carroll's reply, published a week later, answered the "no quantitative predictions" charge with a list:

How about acoustic peaks in the power spectrum of temperature fluctuations in the cosmic microwave background? And the polarization signal, and its spectrum? And the baryon density as deduced from light-element abundances agreeing with that deduced from the CMB? And baryon fluctuations in the power spectrum of large-scale structure? And the transition from acceleration to deceleration in the Hubble diagram of high-redshift supernovae? And the relativistic time delay in supernova light curves?¹¹⁵

He also caught Eric Lerner, the letter's organiser, in a straightforward physics error. Lerner had argued that dark energy violates conservation of energy. Carroll: "there is a field of physics in which energy is not conserved: it's called general relativity."¹¹⁵ Every redshifted photon loses energy while the photon count stays the same. This is old, observed, and has nothing to do with dark energy.

But Carroll's reply is a two-edged exhibit and this article prints both edges. The letter's sociological complaint was that dissent is not tolerated. Carroll's answer was, in substance, correct and rightly so:

And yes, young people who disbelieve in the Big Bang are unlikely to get invited to speak at major conferences, or get permanent jobs at research universities. Likewise astrophysicists who believe in astrology, or medical doctors who use leeches to fight cancer.¹¹⁵

And: "the alternatives to the Big Bang are just silly… They just aren't, for the most part, very smart."¹¹⁵

The signatories were entitled to treat that as confirmation of their complaint. What makes it defensible is not a denial of the fact but the reason Carroll gives — finite resources, and a theory with a very long record of successful prediction. That is a real argument. It is also exactly what a field would say if it were wrong, which is why the argument has to be settled on the evidence rather than on the sociology.

And one honest note about Lerner. He is not an amateur: he is a working experimental plasma physicist with refereed papers in Physics of Plasmas. He published a real, sole-authored MNRAS paper in 2018 arguing that galaxy sizes contradict expansion. It has twenty-seven citations, mostly in alternative-cosmology venues, and no published rebuttal.¹¹⁶ The substantive answer is the same as the answer to López-Corredoira's angular-size test — galaxy size evolution at fixed mass is now measured directly rather than assumed — but the article should say plainly that this specific paper has not been answered in print. His widely circulated JWST claim, by contrast, appeared in a magazine, not a journal.

Michael Disney's parameter-counting argument, and why it no longer works

Michael Disney is a Cardiff astronomer who co-discovered the optical pulsations of the Crab pulsar and worked on Hubble's Faint Object Camera. He is not a crank, and his layered description of the model — quoted in Part 1 — is the most useful thing any critic has written on this subject.

His central technical argument is that cosmology has more free parameters than independent measurements. That argument was weak when he made it and is now clearly wrong. He counts 18 parameters and 17 independent measurements. Base ΛCDM has six parameters. Andrew Liddle had published an information-criteria analysis three years before Disney's 2007 piece arguing that five suffice. Against those six sit thousands of independent measurements: temperature, polarization and lensing power spectra across three thousand multipoles, acoustic oscillations at a dozen redshifts, over a thousand supernovae, weak lensing, cluster counts, and the light-element abundances.

And one of Disney's arguments should not be used by this site at all. He suggests that cosmology's status as a science is compromised because there is only one universe. Milan Ćirković's published reply is the obvious one, and it lands on us:

Per analogiam, it is highly uncertain whether evolutionary biology is a science (there has been only one, unrepeatable evolution of terrestrial biosphere), whether history is a science (unrepeatable sequence of historical events), whether geology is a science (only one Earth!), whether archaeology is a science…¹¹⁷

Anyone making the "you can only do this once, so it isn't science" argument against cosmology has handed the same weapon to someone making it against historical geology, against biblical archaeology, and against the historical case for the resurrection. Use Disney's layering. Leave his demarcation argument alone.

Arguments that are simply dead

The Sunyaev-Zel'dovich shadow is missing — withdrawn by its own author. John Hartnett made this argument in 2006 and retracted it in Journal of Creation in 2018, after a 2013 paper traced the missing shadows to radio emission from the clusters themselves: "At best this no-shadow argument is now equivocal and hence I suggest that it should no longer be used as an argument against the big bang hypothesis."¹¹⁸ Creation Ministries International hosts it under a slug that reads, literally, cmb-shadows-argument-do-not-use. Writers who retract their own arguments in print deserve credit, and this article gives it.

Redshifts are quantised — dead, and again a creationist killed the best case. The strongest version, periodicity in Sloan quasar number counts, was retracted in effect by Hartnett himself in 2009 when he found the same periods in the survey's own reliability flag: "these redshift periods must result from some selection effect… It does not signal any intrinsic (quantized) redshifts in the quasars."¹¹⁹

There is also an argument creationists should make and do not: quantisation would destroy the static-space Doppler model too, since that model needs a smooth monotonic velocity-distance relation.

But "dead" needs splitting into three claims, because they are not equally dead.

Quasar redshifts cluster at preferred values. Tested on 85,000 quasars from modern surveys with no evidence found, and — as with the Sloan number counts — the strongest version was traced to a selection effect. Dead. And even if it were true it would say something about quasars, not about the Hubble relation, which is established from galaxies.

Nearby galaxies prefer multiples of about 72 km/s. This was William Tifft's original claim. It is irrelevant rather than refuted: 72 km/s corresponds to roughly one megaparsec, which is about the distance to the nearest large galaxy. Nobody claims the universe is smooth on that scale. A one-megaparsec box is roughly the volume a galaxy has to sweep up to build itself, so structure at that separation is exactly what the standard model expects. A 1996 study also failed to reproduce the effect with better data.

Galaxies prefer redshifts spaced by hundreds of megaparsecs. This is the version with teeth, first claimed by Broadhurst and colleagues in Nature in 1990 from 396 galaxies, at a spacing of 180 Mpc. It has not reappeared in the far larger surveys that followed. Barnes and Lewis, who are not sympathetic to the claim, still concede that "these matters are still under discussion by cosmologists. Opinions are not settled."¹⁹ Worth knowing: there is a real preferred scale in the galaxy distribution near 150 Mpc, and it is the baryon acoustic oscillation of Part 2 — a broad feature, and a prediction of expansion rather than a problem for it.

Gigaparsec structures violate homogeneity — dead. The Huge Large Quasar Group, the Giant Arc and the Giant Ring of gamma-ray bursts were each announced as too large for the standard model. Each collapsed. The discovery algorithm finds larger "structures" in pure random noise, and standard-model simulations produce patterns like the Giant Arc routinely. The discoverers conceded the mechanism in 2026.

The lithium-6 problem — dead, and the article that uses it contradicts itself. Claimed lithium-6 detections in metal-poor stars turned out to be an artifact of how convection distorts spectral line shapes. The Institute for Creation Research's article on this cites the very LUNA experiment that closed the anomaly, writes "their experiment succeeded," and then asserts in the next paragraph that "the universe has way too much lithium-6 than the Big Bang could produce."¹²⁰ A skeptic will find that in one reading. Lithium-7 is a real problem; lithium-6 is not.

The magnetic monopole problem — not a problem, and not a success either. Inflation is usually credited with solving three problems: flatness, the horizon, and monopoles. But the monopole problem exists only if grand unified theories are true, and no such theory has been confirmed. Proton decay, which every one of them predicts, has never been seen; Super-Kamiokande's limit is past 10³⁴ years.¹²¹ A problem whose premise is unverified physics cannot be cited as a defect in the standard model — or counted as a success when inflation removes it.

The Big Bang violates conservation of energy — true, useless, and it cuts against the person making it. Energy is not globally conserved in general relativity in an expanding universe. This is old news and has nothing to do with the Big Bang in particular. Any cosmology in which light redshifts as it crosses a curved or expanding spacetime has the same feature.

Two claims that are dormant rather than refuted

Honesty requires distinguishing "answered" from "ignored."

Gerrit Verschuur's claim that microwave-background structure correlates with nearby galactic hydrogen was contested by Land and Slosar in 2007, who found "no statistically significant correlation." His later papers have almost no citations. But that is not the same as a refutation, and part of what he found is real: hydrogen filaments genuinely do trace the polarized dust emission that Planck measures, a result now used to build foreground templates.¹²²

The decisive argument is one neither side ran. Galactic gas a hundred parsecs away cannot be gravitationally lensed by clusters at redshift 0.5 to 5. The microwave background is. And local hydrogen radiates in narrow spectral lines; the background is a blackbody across more than two decades of frequency.

Lerner's 2018 galaxy-size paper passed MNRAS refereeing and has never been rebutted in print. So has López-Corredoira's 2017 review, and Disney's 2007 essay. "Nobody has refuted it" is true of all three and misleading about all three: a catalogue of problems has no single claim to reply to, and the individual claims have been closed one at a time in the primary literature. Say "answered piecemeal." Never say "never refuted."

Part 5 — What a Christian must, and need not, accept

The history is the reverse of what most people assume

The expanding-universe solution with a beginning was published in 1927 by Georges Lemaître, a Belgian Catholic priest who was also a trained astronomer. Two years before Hubble's paper he derived the velocity-distance relation from real nebular data and put a number on it: 625 km/s per megaparsec.²¹ In 1931 he proposed that the universe began from a single quantum — the "primeval atom."

That 1931 letter is the founding document of Big Bang cosmology. It runs to three paragraphs. It does not mention God, Genesis or creation. It is a purely physical argument answering a purely physical objection, written by a priest. Lemaître went further: according to the Lemaître Archives he struck a sentence about God out of the manuscript before publishing it.¹²³

The name "Big Bang" was coined by Fred Hoyle, an atheist, in a BBC radio broadcast on 28 March 1949. A popular story says he meant it as mockery. Helge Kragh, the historian of the controversy, finds no evidence for that: "there is no documentation in the historical records for this often repeated view," and Hoyle did not use the phrase at all between 1950 and 1965.²⁰ Hoyle's own explanation was that radio gave him "no visual aids, nothing except the spoken word," and he was reaching for an image.²⁰

But Hoyle did dislike the theory, and he said why, in print, twice. In 1950:

On scientific grounds this big bang assumption is much the less palatable of the two. For it is an irrational process that cannot be described in scientific terms… On philosophical grounds too I cannot see any good reason for preferring the big bang idea.¹²⁴

And in his 1994 autobiography: "Big-bang cosmology is a form of religious fundamentalism."⁶⁶

So: the theory was proposed by a priest who refused to make theology of it, named by an atheist who rejected it on philosophical grounds, and resisted in the Soviet Union as a religious "fairy tale of the origin of the world from nothing."⁶⁴ Whatever else is true, "the Big Bang is a story atheists invented to avoid God" is history backwards.

A quotation this movement should stop using

Arthur Eddington is regularly quoted as saying "the notion of a beginning is repugnant to me." He did write something like it, in Nature on 21 March 1931, page 450. Here is the full passage:

I have no 'philosophical axe to grind' in this discussion. Philosophically, the notion of a beginning of the present order of Nature is repugnant to me. I am simply stating the dilemma to which our present fundamental conception of physical law leads us.¹²⁵

Three things get cut. The disclaimer that he has no axe to grind — which is the very bias the quotation is used to prove. The qualifier "of the present order of Nature," which is not a beginning of everything, and which is exactly the loophole Lemaître exploited in reply. And what follows, where Eddington concedes that the evidence points to a boundary: "we find the sweepings all piled up like a high wall and forming a boundary — a beginning of time — which we cannot climb over."¹²⁵

The full version is better evidence than the truncation, because it shows a reluctant witness conceding. Print the paragraph or do not use it.

The 1951 episode, and what a pope did about it

On 22 November 1951, Pope Pius XII told the Pontifical Academy of Sciences that modern cosmology confirmed "the well-founded deduction as to the epoch when the world came forth from the hands of the Creator," and concluded: "Hence, creation took place. We say: therefore, there is a Creator. Therefore, God exists!"⁶⁴

Lemaître was not happy. Kragh's account:

Lemaitre, whose theory of the primeval universe formed the backbone of the pope's argument, was not at all happy with the address. Himself a Catholic priest and high-ranking member of the Pontifical Academy, Lemaitre believed that astronomy and theology were two separate contexts which should not be mixed; He also felt that the big-bang theory was still a hypothesis, and that the pope had presented it in a much too authoritative way.⁶⁴

He intervened together with Daniel O'Connell, the director of the Vatican Observatory. "Never again did Pope Pius XII try to make cosmology support Christian dogma."⁶⁴

In 1988 John Paul II issued the warning directly: Christianity "possesses the source of its justification within itself and does not expect science to constitute its primary apologetic," and he cautioned specifically against "making uncritical and overhasty use for apologetic purposes of such recent theories as that of the 'Big Bang' in cosmology."⁶⁴

What is actually at stake

The disagreement between a young-earth Christian and standard cosmology is not about expansion, or the microwave background, or the light elements. Every one of those is compatible in principle with a created universe; the model describes how things developed, not who started them.

The disagreement is about time. The standard model says 13.8 billion years. A young-earth reading of Genesis says thousands. That is a real conflict and no amount of goodwill dissolves it.

Two facts have to be kept apart, and confusing them is the commonest mistake in this literature.

The universe is very large, and light takes a long time to cross it. This does not follow from the Big Bang model. It follows from distance measurements and the finite speed of light. Every young-earth cosmology on the market accepts the distances. Jason Lisle puts the star count at "10²², or ten billion trillion, give or take a factor of ten or so."¹²⁶ Danny Faulkner says plainly that measurement errors "would not reduce the distances down to just thousands of light-years."¹²⁷
The universe's contents evolved over that time. This is the model's claim, and the one a young-earth position denies.

Refuting the Big Bang would not shrink the universe by one light-year.

Young-earth astronomers disagree with each other, sharply, in print

There is no single creationist position.

Danny Faulkner argues that young-earth creationists should accept universal expansion and cosmological redshifts — and his 2018 paper in Answers Research Journal is aimed squarely at his own side. He gives four reasons for the resistance: ignorance of the data, so that "this resistance is decades out of date"; "a certain amount of herd mentality"; a reflex he summarises as "If'n he's fer it, then I'm agin it!"; and the fact that "denial of an expanding universe is a short-cut to undermining the big bang model."⁴

His central claim is the one that should give the movement pause:

Therefore, denial of the expansion of the universe interpretation of the Hubble relation amounts to a denial of general relativity. This is profound, because some recent creationists who doubt that the universe is expanding appear to have no problem with general relativity.⁴

He also dismantles Halton Arp, the astronomer most quoted by creationists on discordant redshifts: "it appears that Arp cherry-picked many of his examples… Again, Arp believed that most redshifts were cosmological, but that there were exceptions. Who was to decide what the exceptions were? Well, of course, Arp decided."⁴ And he points out that Arp never doubted the universe was expanding.

And his warning:

This short-cut way of undermining the big bang model could be a huge mistake, for if the universe is expanding, but we reject this, it would be impossible to construct a correct biblical cosmology.⁴

Answers in Genesis contradicts itself on this. It still hosts, as current content, Faulkner's own 2004 chapter "Problems with the Big Bang," which endorses Arp, treats redshift quantisation as a live problem, and says "As the first data from COBE were assembled in the early 1990s, we found that the CBR was perfectly smooth."¹²⁸ That last claim is simply false — COBE detected the anisotropies, work that won the 2006 Nobel Prize. The 2018 paper and the 2004 chapter contradict each other and the earlier one has not been withdrawn or annotated.

The Institute for Creation Research takes the hardest line, and its clearest statement of the case is Jake Hebert's: "There are three main arguments for the Big Bang model… Not a single one of these is an unqualified success."⁴² ICR still circulates the 2004 dissident open letter approvingly, twenty-two years on.

Jason Lisle argues from observability rather than anomalies, and his strongest card is the matter-antimatter asymmetry — which Part 3 agrees is a genuine unsolved problem. His inference does not follow, though: the observed asymmetry is not "100 percent matter versus 50/50," it is one part in a billion surviving annihilation, and that number is measured independently two ways. His claim that "any universe with an average equilibrium temperature of 2.7 degrees will have a CMB"⁹⁹ misses what has to be explained — a blackbody to fifty parts per million, with acoustic peaks, in a universe that is optically thin.

Hugh Ross and Reasons to Believe argue the opposite — that the Big Bang is evidence for a Creator, and that Scripture taught it first, citing eleven verses about the heavens being "stretched out."¹²⁹ The scientific half of that is uncontroversial; the exegetical half is where it is weakest. The Hebrew "stretching out" language is standard ancient Near Eastern tent imagery — Isaiah 40:22 finishes the simile itself, "and spreads them out like a tent to dwell in" — and reading metric expansion out of it is the same move creationists rightly object to when it runs the other way.

Carl Wieland of Creation Ministries International puts the opposing view memorably: adopting the Big Bang into Christian thought "is like bringing the wooden horse within the walls of Troy," and "Marrying one's theology to today's science means that one is likely to be widowed tomorrow."¹³⁰

Four Christians, four incompatible cosmologies, and all four say so in print. Anyone claiming that the Christian position on the Big Bang is settled has not read the literature.

What a Christian need not accept

Nothing in Scripture requires a static universe, a particular value of the Hubble constant, or a view about dark matter. A Christian who accepts expansion, nucleosynthesis and the microwave background has conceded no doctrine.

What a Christian should not do

Two failure modes are visible in the existing literature, and both cost credibility.

The first is to treat every anomaly in cosmology as a victory. Most of them dissolve. Part 4 lists arguments creationist writers made confidently and that are now dead — several retracted by the creationists who made them, which is to those writers' credit.

The second is to treat the Big Bang as proof of God. A pope warned against exactly this, the theory's own author refused to do it, and the physics does not supply the premises the argument needs.

Objections and responses

"The Big Bang keeps being rescued by new inventions — inflation, dark matter, dark energy. That is not science."

Half right, and it is the best objection in the set. Each of those was added to fix a specific failure, and each is a real cost to the theory's simplicity. But "added to fix a problem" is not the same as "unfalsifiable." Dark matter made a prediction — the height of the third acoustic peak — that was measured afterwards and matched. Dark energy was proposed on the basis of supernovae and then confirmed by two independent probes that did not exist at the time. Inflation is where this objection lands hardest, and Part 3 says so.

The general principle matters more than the particular case. Every successful theory has been patched. Neptune was a patch on Newtonian gravity and it was real; Vulcan was the same kind of patch and it was not. You tell them apart by whether the patch makes a new prediction that could fail.

"Three of its ingredients have never been observed in a laboratory."

True, and it is the strongest single sentence against the model. It should be said that plainly, without inflating it into a refutation. A theory can be right about the phenomena and wrong about the mechanism, and the phenomena here are measured: something bends light around clusters where no visible mass sits, and something is accelerating the expansion.

"The model has more free parameters than measurements."

It had a case in 2000. It does not now. The base model has six parameters, fitted to thousands of independent measurements. Whether one likes the model or not, it is enormously over-determined.

"The Hubble tension shows the model is broken."

It shows the calibration is broken, or one of the measurements is. Both sides give an age near 13 billion years. Neither end is compatible with a young universe.

"Cosmology is not experimental science. You cannot rerun the universe."

Correct, and a genuine limitation. But the same is true of geology, forensic science, archaeology and the historical case for the resurrection, and this site should be careful about an argument that cuts its own throat — see Ćirković's reply to Disney in Part 4. What replaces experiment is prediction of things not yet measured: the acoustic peak positions, the acoustic-oscillation scale, and the deuterium abundance were all exactly that.

"But it all rests on extrapolating physics far beyond where it was tested."

Yes, and the best statement of that comes from a Nobel laureate in the field rather than from a critic. Jim Peebles, in his 2019 Nobel Lecture, on the acoustic-oscillation argument:

That is an extrapolation from the tests in the solar system and smaller, on scales ≳ 10¹³ cm, to the scales of cosmology, ~10²⁸ cm. Would you be inclined to trust an extrapolation of fifteen orders of magnitude?³

The answer the model gives is that the extrapolation makes predictions that could have failed and did not. That is a real answer. It is not a proof, and Peebles is not pretending it is.

"If the universe is 13.8 billion years old, Genesis is false."

This is the real disagreement, and this article does not settle it. What it insists on is that the argument be conducted honestly. Attacking the physics with arguments that have been refuted does not help the theology, and several of the arguments in wide circulation were abandoned by the creationists who invented them.

What would settle things

Cosmology has more decisive tests coming than most fields, which is worth saying to anyone who thinks it is unfalsifiable.

Inflation. A detection of primordial gravitational waves at r ≈ 0.005 would confirm the surviving favourite class of models. A null result at r < 0.002 from LiteBIRD would kill most of them — but not the framework, which is the problem.
Dark matter. Roughly a factor of seven of WIMP parameter space remains before the neutrino floor. After that, this style of experiment is over and the field must either detect a particle by some other route or admit it cannot.
Dark energy. DESI's later data releases will either confirm or dissolve the evolving-dark-energy signal. The 2026 recalibration that cut the significance is a warning against banking on it.
The Hubble tension. Freedman's team and Riess's team disagree about a measurement, not about a theory. One of them is wrong, and better calibrators will show which.
Lithium. Either a stellar-depletion mechanism is demonstrated in old halo stars, or a nuclear rate is found to be wrong, or there is new physics. All three are testable.
Baryogenesis. Electron electric-dipole-moment experiments are closing on the parameter space of electroweak baryogenesis with new physics. Standard leptogenesis is out of reach and likely to stay there.

Two further tests deserve naming, because they are the cleanest untested predictions the model has.

Redshift drift. If the expansion rate changes with time, then the redshift of a given galaxy must change as we watch it. Allan Sandage computed the size of the effect in 1962: about one part in 10¹³ per day.¹⁹ That was hopeless then. It is not now — the precision built for detecting exoplanets by stellar wobble is within reach of it, given decades of patient monitoring of the same objects. Nothing else in cosmology would watch the expansion happen in real time.
The primordial neutrino background. The model predicts a sea of neutrinos at 1.95 K today, cooler than the photons by exactly (11/4)^1/3 because neutrinos decoupled before electron-positron annihilation dumped extra heat into the photons.¹⁹ It has never been directly detected, and with current technology it cannot be. Its indirect effect is measured — the effective neutrino count comes out near three from the light elements and near three from the microwave background — but a direct detection would be a decisive confirmation of the first seconds.

An honest closing

There is a way of arguing about the Big Bang that is common in Christian apologetics and that this article has tried not to do. It collects anomalies, quotes scientists out of context, treats every open question as a crisis, and never mentions that the arguments it is using were retracted by the people who made them.

The record here does not support that approach. Several of the strongest-sounding creationist arguments against the Big Bang are dead, and two of them were killed by creationists. The layers most often attacked — expansion, the light elements, the microwave background — are the best-supported parts of the model. And the layers that really are weak — inflation, dark matter, dark energy, the matter-antimatter asymmetry, the initial state — are weak in ways that mainstream cosmologists state openly in their own journals, which is why the honest quotations in this article mostly come from them.

That leaves a genuine disagreement, and it is about time rather than physics. A young-earth reading of Genesis and a 13.8-billion-year universe cannot both be right. Nothing in this article dissolves that, and pretending otherwise would be its own kind of dishonesty.

What the article does claim is narrower. The way to argue that case is not to attack expansion, which a young-earth astronomer publishing in a young-earth journal calls a denial of general relativity. It is not to attack the light elements, where one parameter is now measured twice by unrelated physics and agrees with itself. And it is not to attack the microwave background, whose blackbody spectrum no known local process can produce.

If there is a young-earth cosmology that works, it will have to accept those three things and explain the time. That is a much harder problem than the one most of this literature is trying to solve, and it is the real one.

One last note, and it cuts in our favour. Barnes and Lewis devote several pages to Russell Humphreys' white-hole cosmology, and they open by refusing the cheap move:

Now, it would be easy to simply dismiss this model because of its religious motivation. But this is at most a reason to be suspicious. It might explain why Humphreys is wrong, but it doesn't explain why his idea is wrong. Wrong scientific ideas aren't wrong because the scientist was biased. They're wrong because the universe isn't like that.¹⁹

They then quote C. S. Lewis on the fallacy — Bulverism, assuming a man is wrong and then busily explaining how he got so silly — and go on to test Humphreys' model on its physics, where it fails on grounds first pressed by another young-earth creationist.¹⁹

That is the standard this article has tried to meet in the other direction. A Big Bang cosmologist does not become wrong by wanting the universe to be old, and a creationist does not become wrong by wanting it young. The universe settles it, and the work is in finding out how.

Sources

1.
Disney, M. J. “Modern Cosmology: Science or Folktale?” American Scientist 95(5):383–385. 2007. An essay in American Scientist by M. J. Disney, professor of astronomy at Cardiff University, who co-discovered the optical pulsations of the Crab pulsar and was a member of the team that built Hubble's Faint Object Camera. His more technical version is "The Case Against Cosmology," General Relativity and Gravitation 32 (2000): 1125–1134, and its arXiv number is astro-ph/0009020, not gr-qc/0009020, which is an unrelated paper. The article quotes his picture of Big Bang cosmology as a building of five stacked floors.
1. 1a.
  “BBC is not a single theory but 5 separate theories constructed on top of one another. The ground floor is a theory, historically but not fundamentally grounded in General Relativity, to explain the redshifts – this is Expansion, which happily also accounts for the Cosmic Background Radiation. The second floor is Inflation… The third floor is the Dark Matter hypothesis… The fourth floor is some kind of description for the 'seeds'… And the fifth and topmost floor is the mysterious Dark Energy idea… Thus the Dark Energy floor could crumble leaving the rest of the building intact. But if the Expansion floor collapsed then the entire edifice above it would founder.” The printed American Scientist wording is "five separate theories." ↩
2.
Cooke, Ryan J. “Big Bang Nucleosynthesis.” Encyclopedia of Astrophysics. Elsevier. 2024. A review chapter that explains how the light elements formed in the first few minutes after the Big Bang and summarizes the measurements of their amounts today. The author made the one-percent primordial deuterium measurement, so this is the observer grading their own field. The article uses it for the author's verdict on deuterium and the microwave background, and for the author's admissions about helium and lithium.
1. 2a.
  “Quite amazingly, the baryon density that is inferred from the seven measures of D/H agrees with the baryon density derived from the cosmic microwave background at one percent precision! The incredible agreement of these two baryon density measures, based on completely independent physics and based on two epochs of the Universe separated by almost 400,000 years, represents a triumph to our cosmological understanding, and is one of the strongest confirmations of the standard cosmological model.” ↩ ↩
2. 2b.
  On helium: “this was one of the first triumphs of BBN calculations, which were able to postdict the mass fraction of ⁴He, giving extra credibility to the idea of a hot Big Bang.” The author chose the word postdict. ↩
3. 2c.
  On the origin of the lithium problem: the first WMAP results. “provided a tight bound on the baryon density, and this revealed that the Spite plateau disagreed significantly with the Standard Model value.” The author adds that remeasurement made it worse: “the improved models have made the disagreement with the Standard Model slightly more pronounced… the refined measurements of the reaction rates also made the disagreement even more pronounced.” ↩
3.
Peebles, P. J. E. “How Physical Cosmology Grew.” Nobel Lecture. Dec 8, 2019. The Nobel Prize lecture Peebles gave on 8 December 2019, recalling the steps toward today's standard cosmology. He began studying the large-scale universe in 1964, on the advice of Robert Dicke. The article uses it for Peebles's own description of the BAO theory, the model of sound waves in the early universe, as an extrapolation of standard physics across fifteen orders of magnitude.
1. 3a.
  “The BAO theory assumes standard physics, including the general theory of relativity. That is an extrapolation from the tests in the solar system and smaller, on scales ≳ 10¹³ cm, to the scales of cosmology, ~10²⁸ cm. Would you be inclined to trust an extrapolation of fifteen orders of magnitude?” ↩ ↩
4.
Faulkner, Danny R. “The Case for Cosmological Redshifts.” Answers Research Journal 11:31–47. 2018. A 2018 paper by Dr. Danny R. Faulkner in Answers Research Journal that argues for cosmological redshifts. The article uses it because it argues against the resistance to expansion among creationists, written by one of their own.
1. 4a.
  Page 44: His four reasons for creationist resistance. “most recent creationists appear to be ignorant of the tremendous amount of data that has accumulated over the past half century… Hence, this resistance is decades out of date”. “there is a certain amount of herd mentality”. “'If'n he's fer it, then I'm agin it!'” “denial of an expanding universe is a short-cut to undermining the big bang model.” ↩
2. 4b.
  Pages 45–46: “This short-cut way of undermining the big bang model could be a huge mistake, for if the universe is expanding, but we reject this, it would be impossible to construct a correct biblical cosmology.” ↩
3. 4c.
  Page 45: “it appears that Arp cherry-picked many of his examples of supposedly interacting objects with discordant redshifts. Again, Arp believed that most redshifts were cosmological, but that there were exceptions. Who was to decide what the exceptions were? Well, of course, Arp decided.” Page 44: “Arp and other astronomers who questioned whether quasars had cosmological redshifts never doubted that the universe was expanding.” ↩
4. 4d.
  Page 44: “Therefore, denial of the expansion of the universe interpretation of the Hubble relation amounts to a denial of general relativity. This is profound, because some recent creationists who doubt that the universe is expanding appear to have no problem with general relativity.” Section Abstract, page 31: “There are good reasons for accepting all three… Rejection of cosmological redshifts could stifle development of a true biblical cosmology.” ↩ ↩
5.
Yeh, Tsung-Han et al. Big bang nucleosynthesis analysis. 2026. A 2026 analysis of big bang nucleosynthesis, the theory of how the first light elements formed, by Tsung-Han Yeh, Keith A. Olive, Brian D. Fields and others. It measures the cosmic baryon density, the amount of ordinary matter, from deuterium in twelve quasar absorbers, and compares that with the value from the microwave background. The article uses it for the two independent measurements of that density, which differ by 0.13 percent.
1. 5a.
  Table 1: Deuterium in twelve quasar absorbers plus laboratory nuclear rates, with no CMB input, gives Ω_b h² = 0.02227 ± 0.00043. The CMB acoustic peaks, with no light-element input, give 0.02230 ± 0.00021. Their abstract states the parameter counting outright: “the single free parameter is the cosmic baryon density; the CMB measures this independently, with results consistent with each other.” An earlier formal test allowing the two epochs to have different baryon-to-photon ratios measured the difference as Δη₁₀ = 0.095 ± 0.169 — consistent with zero, allowing at most a ~5% change. A competing nuclear-rate treatment by Launders et al. (2026) widens the disagreement to ~2σ. ↩ ↩
6.
Fixsen, D. J. et al. “The Cosmic Microwave Background Spectrum from the Full COBE FIRAS Data Set.” Astrophysical Journal 473:576. 1996. A paper by a NASA Goddard team that reanalyses the low-frequency data from the ten-month mission of FIRAS, the instrument aboard the COBE satellite that compared the sky with a precise blackbody. It sets tight limits on how far the background spectrum departs from a perfect blackbody. The article relies on those limits for how closely the microwave background matches a perfect blackbody. Mirror: arXiv
1. 6a.
  Section Abstract: “We find new tighter upper limits on general deviations from a blackbody spectrum. The RMS deviations are less than 50 parts per million of the peak of the CMBR. For the Comptonization and chemical potential we find |y| < 15 × 10⁻⁶ and |μ| < 9 × 10⁻⁵ (95% CL).” The earlier Mather et al. 1994 limits (|y| < 2.5 × 10⁻⁵, |μ| < 3.3 × 10⁻⁴) are looser and should not be mixed with these. ↩ ↩
7.
Qu, Frank J. et al. “The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and Its Implications for Structure Growth.” Astrophysical Journal 962:112. 2024. The Atacama Cosmology Telescope (ACT) Collaboration's measurement of how much the gravity of intervening matter bends the microwave background, using five seasons of ACT data. The team reports the lensing signal at 2.3% precision and 43σ significance. The article uses it for that 43σ detection. Mirror: arXiv
1. 7a.
  From the abstract. “We determine the amplitude of the CMB lensing power spectrum at 2.3% precision (43σ significance).” The authors add: “This signal-to-noise ratio independently matches the 42σ achieved in the latest Planck lensing analysis and is competitive with the precision achieved in any galaxy weak lensing analysis.” ↩ ↩
8.
Hilton, Matt et al. The Atacama Cosmology Telescope: DR6 Sunyaev-Zel'dovich Cluster Catalog. Jan 26, 2026. A catalog paper from the Atacama Cosmology Telescope team, covering 16,293 square degrees of sky with data gathered from 2008 to 2022. It lists 10,040 galaxy clusters, each found because the hot gas inside it scatters the background microwave light, which is how the survey detects it. The article uses the catalog for the number of clusters found this way and for the authors' check against the standard model. The version cited is the third arXiv version, dated 26 January 2026.
1. 8a.
  Section Abstract: “We report redshifts and mass estimates for 10040 clusters detected via their Sunyaev-Zel'dovich (SZ) effect with signal-to-noise greater than 4 at a 2.4 arcminute filter scale. The catalog includes 1180 clusters at redshifts greater than 1, and 124 clusters at redshifts greater than 1.5.” The authors also ran a falsification test and report that the standard model passed it. “we find no cluster with a mass and redshift combination high enough to falsify the standard ΛCDM cosmology with Gaussian initial perturbations.” ↩ ↩
9.
BICEP/Keck Collaboration. “Improved Constraints on Primordial Gravitational Waves using Planck, WMAP, and BICEP/Keck Observations through the 2018 Observing Season.” Physical Review Letters 127:151301. 2021. A 2021 analysis by the BICEP/Keck collaboration of microwave polarization from telescopes at the South Pole, combined with Planck and WMAP data through the 2018 season. It sets r_0.05 < 0.036 at 95% confidence, with σ(r) = 0.009, on the gravitational waves that inflation predicts, and the article uses it as the best current limit. Nothing has superseded it as of August 2026, and CMB-S4, whose design goal was σ(r) = 0.0005, lost joint DOE and NSF support on 9 July 2025. ↩ ↩
10.
Steinhardt, Paul J. “Big Bang blunder bursts the multiverse bubble.” Nature 510:9. Jun 3, 2014. A one-page "World View" column in Nature by Paul Steinhardt, a physicist at Princeton University, written after the BICEP2 team announced in March 2014 that it had detected gravitational waves from the early universe. He argues that a Princeton reanalysis showed the signal could come mostly or entirely from galactic dust and other foreground effects, and that inflation is so flexible that no experiment can test it. The article uses it as the strongest wording of the charge that inflation is untestable.
1. 10a.
  “The inflationary paradigm is fundamentally untestable, and hence scientifically meaningless.” ↩ ↩
11.
Clowe, Douglas et al. “A Direct Empirical Proof of the Existence of Dark Matter.” Astrophysical Journal Letters 648:L109. 2006. A weak-lensing study of the merging galaxy cluster 1E0657-558, the Bullet Cluster. The team maps the cluster's mass from how it bends the light of background galaxies, then compares that map with where the hot gas sits. The authors say the mass offset they measure is 8σ, which they argue a change in the law of gravity cannot explain. The article uses it for its claim that the Bullet Cluster shows unseen mass at 8σ using only general relativity.
1. 11a.
  “An 8σ significance spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law.” ↩ ↩
12.
LUX-ZEPLIN Collaboration. “Dark Matter Search Results from 4.2 Tonne-Years of Exposure of the LUX-ZEPLIN (LZ) Experiment.” Physical Review Letters 135:011802. 2025. A search for dark matter particles, called WIMPs, with the LUX-ZEPLIN detector, a two-phase xenon detector, over 4.2 tonne-years of exposure (one tonne of xenon watched for one year). It finds no evidence for an excess over the expected background, and it sets world-leading limits on how often a WIMP would hit a xenon nucleus. The article uses it for that limit and for the point that these searches are running out of room.
1. 12a.
  2.2 × 10⁻⁴⁸ cm² at 40 GeV (published v3; the arXiv v1 gives 2.1 × 10⁻⁴⁸ at 36 GeV). XENONnT reaches 1.7 × 10⁻⁴⁷ and PandaX-4T 1.6 × 10⁻⁴⁷. LZ has separately reported 4.5σ evidence of solar boron-8 coherent neutrino scattering (arXiv:2512.08065, PRL 2026), which is the irreducible neutrino fog floor; roughly a factor of seven of parameter space remains at 40 GeV. ↩ ↩
13.
Weinberg, Steven. “The cosmological constant problem.” Reviews of Modern Physics 61(1):1–23. 1989. A review article by Steven Weinberg of the University of Texas at Austin, based on lectures he gave at Harvard in 1988. It explains that astronomy shows the cosmological constant, the energy of empty space, is many orders of magnitude smaller than modern particle theories estimate, then reviews the history of the problem and surveys five approaches to solving it. The article uses it for the size of the gap between theory and observation.
1. 13a.
  “theoretical expectations for the cosmological constant exceed observational limits by some 120 orders of magnitude,”. “the two terms here must cancel to better than 118 decimal places.” Quantum chromodynamics alone requires 41 orders of cancellation. ↩ ↩
14.
Composite of the current nucleosynthesis literature. n.d. A summary of several papers rather than one, giving a lithium-7 deficit of a factor of 3.3 at 4.4σ, and saying the nuclear-rate resolution has been closed experimentally. Molaro et al. (2024) re-analysed the Small Magellanic Cloud interstellar lithium measurement of Howk et al. (Nature 489:121, 2012) in a way that now cuts against the stellar-depletion explanation, so Howk 2012 must not be cited alone. The article uses it for the lithium-7 failure, a factor of 3.3 at 4.4σ that twenty years of work have not fixed. ↩ ↩
15.
Canetti, Laurent et al. “Matter and Antimatter in the Universe.” New Journal of Physics 14:095012. 2012. A review of the evidence that the early universe kept slightly more matter than antimatter, and of the particle physics that could have produced that leftover matter. The authors also present one testable minimal model that they say would explain that matter, neutrino oscillations and dark matter together. The article uses it for its statement that no accepted explanation of the matter-antimatter asymmetry exists.
1. 15a.
  Section IV.1: The authors take the Jarlskog determinant divided by the sphaleron freeze-out temperature to the twelfth power, which gives. “D/T_sph¹² ~ 10⁻²⁰ ≪ η. Though not a direct proof of impossibility, the smallness of this result makes baryogenesis within the SM very challenging.” Also: “A first order phase transition could only occur if the Higgs mass were below 72 GeV; this is in clear contradiction with experimental data.” ↩ ↩
16.
Csikor, F. et al. “Endpoint of the hot electroweak phase transition.” Physical Review Letters 82:21. 1999. A lattice simulation, meaning a computer calculation on a grid of points, of the electroweak transition, by three physicists from Budapest, Tsukuba and Münster. It finds the transition is first order, the boiling kind, only for a Higgs boson lighter than 72.4 ± 1.7 GeV, and that the LEP lower bound on the Higgs mass rules out any such transition in the Standard Model. The article uses the 72.4 GeV figure because the measured Higgs mass, 125.1 GeV, is above it. Mirror: arXiv
1. 16a.
  Section Abstract: “We obtain that the Higgs-boson endpoint mass in the Standard Model is 72.4 ± 1.7 GeV. Taking into account the LEP Higgs-boson mass lower bound excludes any electroweak phase transition in the Standard Model.” Written before the Higgs was found; the measured mass is 125.1 GeV. ↩ ↩
17.
Penrose, Roger. The Road to Reality: A Complete Guide to the Laws of the Universe. Jonathan Cape. 2004. A book by Roger Penrose on the laws of the universe. Its critique of inflation is in section 28.5, pages 753–757. The article uses it for Penrose's objection that the processes inflation relies on do not explain the Second Law of thermodynamics, because they use it.
1. 17a.
  Section 28.5, page 757: “All spontaneous symmetry-breaking processes and all phase transitions (these being needed for inflation) take place only by the good grace of the Second Law. These processes do not explain the Second Law: they use it.” Section 28.5, page 755: “if the thermalization is actually doing anything… then it represents a definite increasing of the entropy. Thus, the universe would have been even more special before the thermalization than after.” ↩ ↩
2. 17b.
  Section 28.5, page 753: “my remarks do not tell us that inflationary cosmology is wrong. They merely provide strong reasons to doubt most of the initial motivations behind the inflationary idea”. “inflationists have made some definite predictions which, in recent years, have measured up remarkably well.” ↩
18.
Verde, Licia et al. “A tale of many H₀.” Annual Review of Astronomy and Astrophysics. n.d. A review of the disagreement over the Hubble constant, the number that sets how fast the universe is expanding, by Licia Verde, Nils Schöneberg and Héctor Gil-Marín. The article uses it for that disagreement, which the abstract calls a matter of anchors. Mirror: arXiv
1. 18a.
  Abstract: “It appears to be a matter of anchors: the shape of the Universe expansion history agrees with the model, it is the normalizations that disagree.” ↩ ↩
19.
Barnes, Luke A., and Geraint F. Lewis. The Cosmic Revolutionary's Handbook (Or: How to Beat the Big Bang). Cambridge University Press. 2020. A popular handbook on cosmology (ISBN 978-1-108-48670-5) by two working astronomers, which gives the observations behind the big bang and its dark matter and dark energy, and is candid about where the model is weak. Barnes is a postdoctoral researcher at Western Sydney University with a Cambridge PhD in astronomy, and Lewis is Professor of Astrophysics at the Sydney Institute for Astronomy. The book is written to help critics of the standard model attack it properly, and the article relies on it for the authors' admissions about the dark sector, the Tolman test and the CMB temperature.
1. 19a.
  Pages 63–64: On why no material can produce a uniform shift: “to achieve a uniform shift, we need Morphium to absorb wiggles of all sizes, and re-emit this light stretched by a fixed amount. Morphium must be perfectly accommodating: its wiggles must be determined only by the light it absorbs. Any personality, any quirk, any internal property of Morphium that imprints on the wavelength of the re-emitted light will ruin the required uniform shift. But that's the problem. Because the internal parts of Morphium are electrically charged – as they must be to affect light at all – they will interact with each other… There just isn't a way to make a uniform light stretcher out of matter.” ↩
2. 19b.
  Page 113: “But let's be very clear about one point. The big bang theory does not predict the temperature of the CMB. There is no calculation within the big bang theory that produces the number 2.725 K.” “The big bang theory doesn't predict the temperature of the CMB today because today keeps changing.” ↩
3. 19c.
  Page 114: “The reason that the big bang's absence of a prediction for the CMB temperature hasn't counted much against it is because no plausible alternative cosmology has predicted a perfect blackbody spectrum at 2.725 K.” They also issue the challenge directly: “Pay attention, cosmic revolutionary. If your theory can neatly and naturally predict uniform blackbody background radiation with temperature equal to 2.725 K, then it will have scored a win over the big bang theory.” ↩
4. 19d.
  Page 105: “A decade later, Nobel Prize-winner Gerhard Herzberg noted McKellar's observations. In his textbook on molecular spectra, he comments that the inferred temperature of the bath of photons 'has, of course, only a very restricted meaning.'” Their endnote gives the source as Herzberg, Molecular Spectra and Molecular Structure (Princeton: D. Van Nostrand, 1950), p. 496. This corrects a misattribution that circulates widely, including in Peebles 2014, which assigns the sentence to McKellar 1941. ↩
5. 19e.
  Page 97: “we'd prefer to say that the big bang survives the surface brightness test. It doesn't fail, because there are reasonable assumptions that we can make about the universe that render the data consistent with our theory. But it doesn't pass with flying colours either.” They also say plainly: “Cosmologists aren't exactly enthusiastic about the surface brightness (Tolman) test.” ↩
6. 19f.
  Pages 226–227: The Big Bang's explanations of the darkness of the night sky, Hubble's Law, supernova time dilation, galaxy dimming, the CMB blackbody and temperature-redshift relation, the Lyman-alpha forest and big bang nucleosynthesis: “do not depend on the amount of dark matter and dark energy… the predictions of the big bang model discussed thus far would remain completely untouched if we discovered tomorrow that dark matter and dark energy don't exist.” ↩
7. 19g.
  Page 226: “We find it amusing when critics of the big bang point to the dark sector as if it were some kind of conspiracy, because cosmologists would dump the dark components in a moment. If someone convinced us that the universe could be explained convincingly – without raising even bigger problems – using only ordinary matter, we would gleefully throw all our dark matter and dark energy models in the garbage bin.” ↩
8. 19h.
  Pages 241–242: On redshift drift. Sandage calculated it in 1962 at. “around one part in 10¹³ per day”. beyond the instruments of the time; it was rediscovered by Avi Loeb in the late 1990s and is now called the Sandage-Loeb test. ↩
9. 19i.
  Page 245: The photon background is hotter than the neutrino background. “by a precise factor of (11/4)^1/3, which amounts to about 40%”. This gives an expected neutrino background temperature of 1.95 K today. Their indirect neutrino counts, from the light elements, are. “between 1.9 and 4.5, with the most likely value being about 3.1”. and from the CMB and large-scale structure, they are. “between 2.66 and 3.33, with the most likely value being about 2.99”. ↩
10. 19j.
  Pages 239–240: On the satellite planes: “This was not predicted by any galaxy formation simulation before it was discovered… Placing dwarf galaxies on fine planar orbits is akin to a gorilla repairing a watch; not impossible, but difficult to imagine.” The Andromeda plane is. “36,000 light years thick, but 1,200,000 light years in extent”. with the northern dwarfs approaching and the southern receding, a coherently rotating structure. Lewis was directly involved in the 2014 measurement. ↩
11. 19k.
  Pages 211–214: On redshift quantisation: the 72 km/s claim corresponds to about one megaparsec, and. “The existence of structure on the scale of a few megaparsecs is not at all a problem for the big bang.” Modern quasar surveys (85,000 objects, Repin, Komberg & Lukash 2010) find no preferred redshifts, and Nordgren, Terzian & Salpeter 1996 failed to reproduce the small-scale effect. On the Broadhurst 180 Mpc claim they write: “This claim has bite… These matters are still under discussion by cosmologists. Opinions are not settled”. while noting that later, larger surveys have not reproduced the picket-fence structure, and that the one real preferred scale is the ~150 Mpc baryon acoustic oscillation. ↩
12. 19l.
  Page 218: On Russell Humphreys' white-hole cosmology: “Now, it would be easy to simply dismiss this model because of its religious motivation. But this is at most a reason to be suspicious. It might explain why Humphreys is wrong, but it doesn't explain why his idea is wrong. Wrong scientific ideas aren't wrong because the scientist was biased. They're wrong because the universe isn't like that.” ↩
13. 19m.
  Page 219: They side with Don Page's technical objection that Humphreys' claimed time dilation does not follow from his own equations, and then give the argument from a fellow young-earth creationist. John Hartnett points out that the extreme spacetime warping the model needs would leave a signature, and light from Andromeda. “arrives at us essentially unchanged, with no sign of redshift or blueshift from intense gravitational fields.” Hartnett: “I don't believe the relative clock rates can be tinkered with to achieve a sensible result.” They also note that Humphreys' model. “invokes only natural laws and natural things,”. so it is testable science regardless of its motivation. ↩
20.
Kragh, Helge. What's in a Name: History and Meanings of the Term 'Big Bang'. 2013. A historical study of the name "big bang" and of what the term meant to the astronomers and physicists who used it, covering finite-age models of the universe from the 1920s to the 1970s. The article uses it for the history of the name: Friedmann's 1922 solutions, Lemaître's 1931 "primeval atom," and the 1949 coinage by Fred Hoyle. Page numbers below are from the 40-page preprint, which was printed in cut form as "Big Bang: the etymology of a name," Astronomy & Geophysics 54, no. 2 (2013): 2.28–2.30.
1. 20a.
  Page 8: “A second misunderstanding is to read the big bang into Friedmann's paper of 1922. Although this paper included big bang solutions, it was in a mathematical sense only (R = 0 for t = 0)… his paper was basically mathematical, with no references to either astronomical measurements (such as the galactic redshifts) or to the physical properties of the universe.” ↩
2. 20b.
  Pages 8–9: “According to his thinking there was no initial zero-volume singularity corresponding to an infinite density, but instead everything began in a material proto-universe of a density of the order of an atomic nucleus and a size comparable to the solar system.” Page 8: “the idea of a big bang was also absent from Lemaître's paper of 1927 and only appeared four years later.” ↩ ↩
3. 20c.
  Page 9: “In his publications on cosmology from 1931 to the early 1960s Lemaître usually referred to his theory by these two names, primeval atom and fireworks. He never used the term big bang, neither for his own theory nor for other theories of the same kind.” ↩
4. 20d.
  Page 41: “Another popular misconception is that Hoyle coined the term to ridicule or disparage theories with a definite origin of the universe, such as Gamow's. Although one cannot rule it out, there is no documentation in the historical records for this often repeated view. … Had Hoyle intended the term in this way, he would presumably have used it frequently during the cosmological controversy, which he did not. Between 1950 and 1965 he did not refer to Big Bang at all.” The coinage was a BBC Third Programme talk on 28 March 1949, printed in The Listener. Page 17: Kragh also establishes that the widely repeated story of Hoyle using the phrase pejoratively. “during a BBC radio debate with Gamow”. is fiction. Kragh says: “There never was such a radio debate between the two cosmologists!” ↩
5. 20e.
  Page 18: Hoyle's own account, in an interview with Alan Lightman on 15 August 1989: “I was constantly striving over the radio – where I had no visual aids, nothing except the spoken word – for visual images. And that seemed to be one way of distinguishing between the steady-state and the explosive big bang. And so that was the language I used.” Gamow disliked the name: “I don't like the word 'big bang' … it is a kind of cliché.” ↩
21.
Lemaître, Georges. “Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques.” Annales de la Société Scientifique de Bruxelles A47:49–59. 1927. A short paper in French by the Belgian Abbé Georges Lemaître. It combines an expanding solution with the velocity-distance law and a numerical expansion rate, derived from 42 nebulae in the lists of Hubble and Strömberg. The article uses it for the first published value of the expansion rate, 625 km/s per megaparsec, two years before Hubble's paper. ↩
1. 21a.
  Page 56: “Utilisant les 42 nébuleuses figurant dans les listes de Hubble et de Strömberg, et tenant compte de la vitesse propre du soleil… on trouve une distance moyenne de 0,95 millions de parsecs et une vitesse radiale de 600 Km./sec, soit 625 Km./sec à 10⁶ parsecs.” Lemaître's own footnote on the same page says: “En ne donnant pas de poids aux observations, on trouverait… 575 Km./sec à 10⁶ parsecs. Certains auteurs ont cherché à mettre en évidence la relation entre v et r et n'ont obtenu qu'une très faible corrélation entre ces deux grandeurs… il semble donc que ces résultats négatifs ne sont ni pour ni contre l'interprétation relativistique de l'effet Doppler.” ↩ ↩
22.
Hubble, Edwin. “A Relation Between Distance and Radial Velocity Among Extra-Galactic Nebulae.” Proceedings of the National Academy of Sciences 15(3):168–173. 1929. A short paper that gives the distances and radial velocities of 24 extra-galactic nebulae, with each distance estimated from the apparent brightness of stars such as Cepheid variables, novae and blue stars. Hubble found that the farther a nebula was, the larger its velocity, a roughly linear relation. The article uses it for that relation, which it says was confirmed, and for Hubble's own reading of it in 1929.
1. 22a.
  Pages 170–171: “let A = 277°, D = +36°… V₀ = 280 km./sec., K = +500 km./sec. per million parsecs.” His K is what is now called H₀, about 7.3 times the modern value. Page 173: “The results establish a roughly linear relation between velocities and distances among nebulae for which velocities have been previously published.” ↩
2. 22b.
  Page 173: “The outstanding feature, however, is the possibility that the velocity-distance relation may represent the de Sitter effect… In the de Sitter cosmology, displacements of the spectra arise from two sources, an apparent slowing down of atomic vibrations and a general tendency of material particles to scatter.” ↩
23.
Einstein, A., and W. de Sitter. “On the Relation between the Expansion and the Mean Density of the Universe.” Proceedings of the National Academy of Sciences 18(3):213–214. Mar 15, 1932. A two-page note in which A. Einstein and W. de Sitter argue that the observed expansion and density can be fitted by a universe with no curvature and no cosmological constant. Their zero-curvature model gives a density of 4 × 10^-28 grams per cubic centimeter at an expansion rate of 500 km/s per megaparsec, which they say may be on the high side but is of the correct order of magnitude. The article uses it for the flat, matter-only model it calls Einstein-de Sitter, which it says was the textbook standard Big Bang for sixty years and is now falsified.
1. 23a.
  Page 213: “There is no direct observational evidence for the curvature, the only directly observed data being the mean density and the expansion… the question arises whether it is possible to represent the observed facts without introducing a curvature at all.” With their assumed expansion rate of 500 km/s/Mpc the model's own age is about 1.3 billion years — younger than the radiometric ages of Earth rocks already known in 1932. ↩
24.
Bondi, H., and T. Gold. “The Steady-State Theory of the Expanding Universe.” Monthly Notices of the Royal Astronomical Society 108:252–270. 1948. A 1948 paper arguing that the universe must be expanding yet can stay the same on large scales, with new matter created continuously at a rate too low to see directly. The authors say all the observational tests they examine agree well with it. The article uses it as the origin of the steady-state model, which it lists as falsified.
1. 24a.
  Page 255: “We do not claim that this principle must be true, but we say that if it does not hold, one's choice of the variability of the physical laws becomes so wide that cosmology is no longer a science. One can then no longer use laboratory physics without relying on some arbitrary principle for their extrapolation.” ↩ ↩
25.
Hoyle, F. et al. “A Quasi-Steady State Cosmological Model with Creation of Matter.” Astrophysical Journal 410:437–457. 1993. A full account of a quasi-steady state model, in which matter is created in bursts spread across all of space and time, with no overall beginning. The authors say the model explains the 2.73 K microwave background and the abundances of the light elements. The article uses it as the 1993 statement of this model in its table of alternatives to the big bang.
1. 25a.
  Section Abstract, page 437: “The model is based on the idea that creation takes place in little big bangs each involving about 10¹⁶ M_⊙ distributed over all space and time, the universe itself being without a beginning.” ↩
26.
Planck Collaboration. “Planck 2018 results. VI. Cosmological parameters.” Astronomy & Astrophysics 641:A6. 2020. The final Planck satellite analysis of the cosmic microwave background, fitting the standard six-parameter model to its temperature, polarization and lensing data. The authors find good consistency with that model and no compelling evidence for extensions to it. The article uses it for the six parameters themselves, the age of the universe, the spectral index, and Planck's decision not to discuss lithium. Mirror: arXiv
1. 26a.
  Table 2: The six base parameters, from Table 2 (TT,TE,EE+lowE+lensing): Ω_b h² = 0.02237 ± 0.00015; Ω_c h² = 0.1200 ± 0.0012; 100θ_MC = 1.04092 ± 0.00031; τ = 0.0544 ± 0.0073; ln(10¹⁰ A_s) = 3.044 ± 0.014; n_s = 0.9649 ± 0.0042. Derived: H₀ = 67.36 ± 0.54; Ω_m = 0.3153 ± 0.0073; σ₈ = 0.8111 ± 0.0060; r_drag = 147.09 ± 0.26 Mpc. ↩
2. 26b.
  Table 2: The age that the fit gives, Age = 13.797 ± 0.023 Gyr (billion years). ↩
3. 26c.
  n_s (the spectral index, which describes how the strength of the ripples changes with their size) = 0.9649 ± 0.0042, which the paper notes is 8σ from scale invariance. ↩
4. 26d.
  Section 7.6: “We do not discuss other light elements, such as tritium and lithium, since the observed abundance measurements and their interpretation in terms of the standard models of BBN are more controversial.” The same section reports: “Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations”. It also gives a CMB-only helium measurement from the damping tail, Y_P = 0.241 ± 0.025, independent of both starlight and nuclear physics. ↩
5. 26e.
  From the abstract. “The CMB spectra continue to prefer higher lensing amplitudes than predicted in base-ΛCDM at over 2σ; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data.” ↩
27.
DESI Collaboration. “DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints.” Physical Review D 112:083515. 2025. The second results paper from the DESI collaboration's DR2 data, which measures baryon acoustic oscillations and the limits they put on cosmological models. Baryon acoustic oscillations are the regular spacing left by sound waves in the early universe, seen in how galaxies are spread out, and they work as a ruler for distance. The article uses it for the evolving dark energy result, which it calls contested, and for the 147.05 Mpc sound-horizon figure that the microwave background fixes. Mirror: arXiv
1. 27a.
  Evolving dark energy is preferred over a cosmological constant at 3.1σ with the CMB alone, 2.8σ with Pantheon+, 3.8σ with Union3 and 4.2σ with DES-Y5. DESI's own caveat is that the 3.1σ falls to 2.4σ with simple priors. Popovic et al. (MNRAS 2026, arXiv:2511.07517) cut the DES-Y5 figure from 4.2σ to 3.2σ on recalibration, and reported. “only a weak preference for evolving dark energy.” ↩ ↩
2. 27b.
  Section §1: “the CMB provides tight constraints on ω_b and ω_bc, leading to a 0.2% determination of r_d… Second, the same physics imprints both the BAO and the acoustic peaks in the CMB power spectrum.” r_d = 147.05 Mpc. ↩
28.
Lemaître, Georges. “A Homogeneous Universe of Constant Mass and Increasing Radius accounting for the Radial Velocity of Extra-galactic Nebulæ.” Monthly Notices of the Royal Astronomical Society 91:483–490. 1931. “From a discussion of available data, we adopt R'/R = 0·68 × 10⁻²⁷ cm.⁻¹”. The translation compresses the whole derivation to this one sentence. The number survived translation; its derivation and Lemaître's own caveats did not. An English translation, published in 1931, of Lemaître's paper in the Annales de la Société Scientifique de Bruxelles. The translation leaves out a passage of the French original, and the article uses this translation to show what was dropped: the derivation of the expansion-rate figure and Lemaître's own caveats. ↩
29.
Faulkner, Danny R. “Misquoting Hubble.” Answers Research Journal 11:221–226. 2018. A young-earth astronomer's paper correcting creationist misuse of Hubble's words. It argues that a truncated quotation, "the unwelcome supposition of a favoured location must be avoided at all costs", reverses Hubble's meaning, because Hubble was stating a hypothesis that he then rejected. The article points readers to it before they repeat the claim that even Hubble doubted expansion. ↩
30.
Peebles, P. J. E. “Discovery of the hot Big Bang: What happened in 1948.” European Physical Journal H 39:205–223. 2014. A 2013 historical review by P. J. E. Peebles of Princeton University, on what the papers of 1948 said about a hot early universe and its leftover radiation. Peebles counts eleven publications from that year and finds that the one most often cited, by Alpher, Bethe and Gamow, assumed a cold Big Bang. The page numbers below are those of the 2013 arXiv preprint. The article uses it for the claim that the Big Bang did not have to be hot, and for what the 1948 papers actually assumed.
1. 30a.
  Page 3: “Alpher, Bethe, and Gamow (1948) assume a cold Big Bang cosmology, and it makes no mention of thermal radiation. Also, the picture in this paper is physically inconsistent. The inconsistency was resolved later that year by the proposal that elements formed in the early universe in a sea of thermal radiation.” ↩
2. 30b.
  Page 20: “The problem with the cold Big Bang picture is that one must postulate some special circumstance that prevents element buildup from happening too early, for otherwise the universe would be left without its most abundant element, hydrogen. The hot Big Bang picture does not have this problem because thermal dissociation by the sea of radiation prevents accumulation of deuterons and their conversion to heavier elements until the temperature has dropped to T_i ≃ 10⁹ K.” ↩
3. 30c.
  Page 19: Quoting Hoyle's 1950 review, Gamow's model. “would lead to a temperature of the radiation at present maintained throughout the whole of space much greater than McKellar's determination for some regions within the galaxy.” ↩
4. 30d.
  Page 15: “the paper Alpher and Herman (1948a) presents the first estimate of the present radiation temperature. Their numerical value is not significant because it depends on the present baryon density, which was very uncertain, and they compute element buildup along the wrong path. Their lasting contribution is the first example of how the theory of what was happening when the expanding universe was a few minutes old may be tested by measurements some 14 Gyr later.” ↩
31.
Aguirre, Anthony. “The Cold Big-Bang Cosmology as a Counter-example to Several Anthropic Arguments.” Physical Review D 64:083508. 2001. A theoretical paper that builds a family of universes on the classical cold big-bang model, with some or all of the basic parameters differing by orders of magnitude from the standard hot big-bang values. It argues that requiring sun-like stars with planets does not fix those parameters, so a very different early universe could still host intelligent life. The article uses it to show that "Big Bang" names a family of models, not one.
1. 31a.
  Section §III and §IV: The standard model has. “η_γ ≈ 2 × 10⁹”. his cold model has. “η_γ ≲ 10.” “For certain combinations of η_γ and η_L, nucleogenesis yields a helium fraction of 25%, just as in the standard HBB. However, for ηγ ≲ 10, nucleogenesis also produces heavier elements (metals), yielding metallicity of Z ≳ 0.1 Z⊙ for a 25% helium yield.” ↩
32.
Hoyle, F. “A New Model for the Expanding Universe.” Monthly Notices of the Royal Astronomical Society 108:372–382. 1948. A theory paper by F. Hoyle with no new observations. It adds the continuous creation of matter to the equations of general relativity, so that the universe can expand while its average density stays the same. The paper checks the model against the velocity-distance relation that Hubble and Humason had found for nebulae. The article uses it for Hoyle's own reason for preferring creation without a beginning.
1. 32a.
  Page 372: “This possibility seemed attractive, especially when taken in conjunction with aesthetic objections to the creation of the universe in the remote past. For it is against the spirit of scientific enquiry to regard observable effects as arising from 'causes unknown to science', and this in principle is what creation-in-the-past implies.” ↩
33.
Ryle, M., and R. W. Clarke. “An Examination of the Steady-State Model in the Light of Some Recent Observations of Radio Sources.” Monthly Notices of the Royal Astronomical Society 122:349–362. 1961. A 1961 observational paper from the Mullard Radio Astronomy Observatory that counts radio sources at fainter flux levels than earlier surveys had reached. It compares the counts with what the steady-state model, the rival theory in which the universe looks the same at all times, predicts, and finds at least 3 ± 0·5 times as many sources at those levels as the model predicts. The article quotes its verdict against the steady-state model.
1. 33a.
  Page 349: From the summary. “A comparison of these observational results with those predicted by the steady-state model shows a marked discrepancy, the number of sources observed with a flux density in the range 0·5 to 2 × 10⁻²⁶ watts (c/s)⁻¹ m⁻² being at least 3 ± 0·5 times that predicted by the model… the results appear to provide conclusive evidence against the steady-state model.” ↩
34.
Lewis, Geraint F., and Brendon J. Brewer. “Detection of the cosmological time dilation of high-redshift quasars.” Nature Astronomy 7:1265–1269. 2023. A 2023 paper that reports (1 + z) time dilation in 190 quasars monitored for two decades. The article uses it to answer the claim that quasars show no time dilation.
1. 34a.
  (1 + z) time dilation detected in 190 quasars monitored for two decades. The paper cites López-Corredoira 2017 directly, closing the "quasars show no time dilation" item on his list. Brewer, Lewis & Li, MNRAS 537 (2025): 809, measure the exponent as n = 1.14 ± 0.34. Earlier supernova results: Goldhaber et al. 2001 (light curves), Blondin et al. 2008 (spectra — the stronger version). ↩ ↩
35.
Noterdaeme, P. et al. “The evolution of the cosmic microwave background temperature.” Astronomy & Astrophysics 526:L7. 2011. A short letter that measures the temperature of the cosmic microwave background at higher redshift, the further back in time, and fits it with a power law. The article uses it as the measurement behind its test that the background was hotter in the past, by a factor of 1 + z.
1. 35a.
  “T_CMB(z) = (2.725 +/- 0.002) x (1+z)^(1-beta) K with beta = -0.007 +/- 0.027.” Sunyaev-Zel'dovich determinations give a joint α = −0.001 ± 0.012 (Hurier 2014, de Martino 2015). ↩
36.
Riechers, Dominik A. et al. “Microwave background temperature at a redshift of 6.34 from H2O absorption.” Nature 602:58–62. 2022. A 2022 Nature paper that measures the microwave background temperature at redshift 6.34 from the absorption of water vapour. The article uses it as a test that the background was hotter in the past.
1. 36a.
  16.4 to 30.2 K (kelvin, 1σ) at z = 6.34, against a predicted 20.0 K. ↩
37.
López-Corredoira, Martín. “Tests and problems of the standard model in Cosmology.” Foundations of Physics 47(6):711–768. 2017. A 2017 review of observations that cause problems for the standard model, by a staff astrophysicist at the Instituto de Astrofísica de Canarias. It runs to 64 pages and 473 references, and the author says he takes no position on whether standard cosmology is correct. The article calls it the most thorough catalogue of the model's problems in print.
1. 37a.
  Pages 2–3: “It is not my purpose to defend a particular theory against the standard cosmology. All theories have their own problems. Only the problems of the standard Big Bang theory are put forward here, but many more affect the alternative models.” ↩
2. 37b.
  Page 3: “It may also be that some of the caveats presented are no longer caveats, or that some of the observational measurements are not correct. Warning: I review only certain critical papers, and in a few cases I discuss them, but I take no responsibility for their contents. In most cases, I collect the information given by the different papers without any further research… My own position is also neutral, I express no opinion on whether the standard cosmology is correct or not.” ↩
3. 37c.
  Page 9: “The CMBR temperature measured from the rotational excitation of some molecules as a function of redshift has been quite successful in proving expansion: the results of Noterdaeme et al. with the exact expected dependence on T = T₀(1 + z) are impressive.” “if we accept these results, at least one can say with almost total confidence that a local origin of the CMBR in a static Universe is excluded.” ↩
4. 37d.
  Page 12: On galaxy number counts: “Differential galaxy number counts vs. galaxy K magnitude are fitted by the standard cosmological model, but also by the tired light Universe. The same problem arises again: degeneracy between evolution and cosmological geometry.” On Lerner's UV surface-brightness test: “Nonetheless, Lerner's hypothesis of a maximum UV SB might be incorrect, so this should be further explored before reaching definitive conclusions about this test.” ↩
5. 37e.
  Page 33: “The quasar population is unlikely to provide enough photons to ionize the universe at z ≈ 6, even less for higher redshift, where there is a lower number of QSOs.” ↩
6. 37f.
  Page 44: In the conclusions: “We must also admit that alternative theories are not at present as competitive as the standard model in cosmology in terms of giving better explanations.” Page 13: His own summary table reads: “Apparently, there is no winner yet. The first two tests favour expansion, whereas the 4-8th tests get a less ad hoc fit with the static solution, although this is insufficient to reject expansion.” ↩
7. 37g.
  Pages 11–12: “all of them, either in the radio, near infrared or visible, show, over a range of up to redshift 3, a dependence θ ~ z⁻¹, a static Euclidean effect over all scales. This result cannot be reconciled with the standard cosmological model unless we assume a strong evolution of galactic radii… galaxies with the same luminosity should be six times smaller at z = 3.2 than at z = 0… However, we must be cautious with this interpretation, because of the uncertainty in the galaxy size evolution.” ↩
38.
Sayers, Jack et al. “A Measurement of the Kinetic Sunyaev-Zel'dovich Signal Toward MACS J0717.5+3745.” Astrophysical Journal 778:52. 2013. A 2013 paper that measures the kinetic Sunyaev-Zel'dovich effect, the small temperature shift that microwave background light picks up from the hot gas of a moving cluster, toward the cluster MACS J0717.5+3745. The article uses it for how fast clusters move relative to the background.
1. 38a.
  Sub-cluster B of MACS J0717.5+3745 (z = 0.5458, its redshift) moves at +3450 ± 900 km/s relative to the microwave background. In a static-space model where the redshift is real motion, that cluster would be receding at about 123,000 km/s and the signal would be roughly 36 times larger. ↩
39.
Etherington, I. M. H. “On the Definition of Distance in General Relativity.” Philosophical Magazine 15:761. 1933. Holanda, Lima and Ribeiro state its modern form in ApJL 722 (2010): L233, §1: “completely general, valid for all cosmological models based on Riemannian geometry, being dependent neither on Einstein field equations nor the nature of matter-energy content.” DESI 2024 baryon acoustic oscillation data plus supernovae match this to about 2 percent. A 1933 paper by I. M. H. Etherington on how distance is defined in general relativity. The article uses it for the point that the dimming of galaxy surface brightness with redshift follows from general relativity alone, so it is not a test of expansion, and works this through in The Doppler Model of Galaxy Redshifts. ↩
40.
Sandage, Allan. “The Tolman Surface Brightness Test for the Reality of the Expansion. V. Provenance of the Test and a New Representation of the Data for Three Remote HST Galaxy Clusters.” Astronomical Journal 139:728. 2010. The last of five papers concluding decades of observational work on the test. It re-reduces Hubble Space Telescope photometry of elliptical galaxies in three clusters at redshifts near z = 0.85, and finds a highly significant Tolman signal, degraded by luminosity evolution, from which it concludes that the expansion is real. The article uses it for Sandage's own verdict on the test.
1. 40a.
  “the Tolman test … has not been quite as easily done as I set out … in 1974. It has required many developments not yet made at the time. However, the test seems to have been successful. The Tolman prediction is verified. The expansion would seem to be real.” The same paper attributes part of the residual to measured luminosity evolution: “0.8 mag in R_cape and 0.4 mag in the I_cape photometric rest-frame bands.” ↩
41.
Lisle, Jason. “Size of Galaxies in JWST Data and Cosmology — Reply to Barnes.” Answers Research Journal 18:441–447. 2025. A 2025 reply by Jason Lisle to Luke Barnes, on the size of galaxies in JWST data and what that means for cosmology. The article uses it because Lisle concedes in print that his Doppler model gives no help with the age of the universe.
1. 41a.
  Page 446: Answering Luke Barnes's point that the Doppler model does not solve the starlight problem: “Quite right. The Doppler model is not needed to explain distant starlight in a young universe. Rather, it was invoked to explain the angular size and luminosity data in JWST deep fields.” He adds that. “since the ASC model doesn't assume any particular metric, it is compatible with either the FLRW metric or the Doppler model.” ↩
42.
Hebert, Jake. “Astronomy Magazine: Big Bang in Crisis?” Creation Science Update, Institute for Creation Research. May 21, 2020. A 2020 article by Jake Hebert of the Institute for Creation Research, responding to a May 2020 Astronomy magazine feature that asked whether the Big Bang is in crisis. It summarizes the three main arguments for the Big Bang and says that none of them is an unqualified success. The article uses it as the Institute for Creation Research's clearest statement of the creationist case.
1. 42a.
  “The Big Bang model has an adjustable parameter, like a tuning knob on a radio, that theoreticians can adjust to ensure that the Big Bang produces the amounts of hydrogen and helium necessary to match observations.” His footnote names it: “This adjustable parameter is called the baryon-to-photon ratio.” ↩
2. 42b.
  “There are three main arguments for the Big Bang model: 1) the apparent expansion of the universe, 2) the ability of the model to account for the relative cosmic abundances of hydrogen and helium, and 3) the existence of the cosmic microwave background (CMB)… Not a single one of these is an unqualified success, and apparent successes often lead to problems for the model!” ↩
43.
Hoyle, F., and R. J. Tayler. “The Mystery of the Cosmic Helium Abundance.” Nature 203:1108–1110. 1964. A short paper that predicted how much helium the early universe made, giving a primordial helium mass fraction of 0.36 ± 0.04, and stated an explicit condition under which the prediction would be falsified. The article sets that figure against the modern value of 0.2458 ± 0.0013 and finds it wrong by more than three of its own error bars. It is cited for the drift of the predicted helium figure over the years. ↩
44.
Peebles, P. J. E. “Primordial Helium Abundance and the Primordial Fireball. II.” Astrophysical Journal 146:542–552. 1966. A 1966 calculation of the helium, helium-3 and deuterium made in the hot early universe. It assumes that the newly found microwave background is the leftover heat of that early stage, at 3 K, and it tries two present mass densities, 7 × 10⁻³¹ and 1.8 × 10⁻²⁹ gm/cm³. The article uses it to show that the density of matter changes the predicted helium very little, from 28 to 26 per cent, when the density is varied by a factor of about twenty-six.
1. 44a.
  “For these models the final helium abundance by mass was found to be 28 per cent if the present mass density is ρ₀ = 1.8 × 10⁻²⁹ gm/cm³, and 26 per cent if ρ₀ = 7 × 10⁻³¹ gm/cm³.” That is a factor of twenty-six in density for a two-percentage-point change in helium. His conclusion also states plainly that the observation did not yet exist: “Apparently a primordial abundance this high cannot yet be ruled out because we do not have a reliable measure of the helium abundance in very old Population II stars.” ↩ ↩
45.
Fields, Brian D. et al. “Big-Bang Nucleosynthesis after Planck.” JCAP (03):010. 2020. A status report by four physicists on how the light elements formed in the first few minutes after the Big Bang, using the final Planck cosmic microwave background data and new nuclear reaction rates (an erratum appeared in JCAP 11 (2020): E02). They find deuterium and helium-4 agree well with observation, while lithium-7 disagrees strongly. The article uses it for that lithium problem and for the authors' claim that the theory now has almost no adjustable number left. Mirror: arXiv
1. 45a.
  Section §II: “Greatly improved measurements of the neutron mean-life, the accurate CMB determination of the baryon density first by WMAP, and the LEP and SLC determinations of the number of neutrinos (in the standard model) from the invisible width of the Z boson, have effectively made BBN a zero-parameter theory.” ↩
2. 45b.
  Figure 4: “We see excellent agreement for D/H, good agreement for ⁴He, and strong discrepancy in ⁷Li constitutes the persistent lithium problem.” Their conclusion: “As much as the concordance between BBN theory, light element abundance observations, and measurements of the CMB is impressive, the elephant in the room is the ⁷Li abundance.” ↩
3. 45c.
  Table II: The abundance sensitivities to the baryon-to-photon ratio η: Y_p ∝ η^0.039, D/H ∝ η^−1.6, ³He/H ∝ η^−0.58, ⁷Li/H ∝ η^+2.1. Their measured neutrino count from BBN alone is N_ν = 2.86 ± 0.15, against 2.859 ± 0.314 from the CMB alone and 2.9963 ± 0.0074 from the Z-boson width at LEP. ↩
46.
Wagoner, Robert V. et al. “On the Synthesis of Elements at Very High Temperatures.” Astrophysical Journal 148:3–49. 1967. A 1967 calculation, by Robert Wagoner, William Fowler and F. Hoyle, of which light elements could form in the early stages of an expanding universe and in exploding supermassive stars. It found that deuterium, helium-3, helium-4 and lithium-7 can be made in the universal fireball, with reasonable agreement with solar-system abundances if the present temperature is 3 K and the present density is at most about 2 × 10^-31 g/cm^3. The article uses it for its helium prediction, its density estimate and its lithium-7 error, each compared with today's values.
1. 46a.
  Section §X, Conclusion 1, page 42: “The mass fraction of He⁴ produced lies between 0.2 and 0.3 for the universal fireball (assuming T₀ = 3° K), but can be higher in a massive object. It is therefore of great importance to determine helium concentrations in different astronomical bodies. A confirmation of X(He⁴) ≈ 0.4 for B stars and for some planetary nebulae could point toward massive objects as the site of origin for the helium. On the other hand, if it could be shown that X(He⁴) is always close to 0.27, this would be evidence favorable to a universal fireball.” Section Conclusion 10, page 43: The authors add their own caveat: “The evidence on this point is not unequivocal, however.” ↩
2. 46b.
  Page 24: “For θ = 1 and h = 7 × 10⁻⁶, ρ₀ ≈ 2 × 10⁻³¹ gm cm⁻³, very near the estimated 3-7 × 10⁻³¹ gm cm⁻³ for the average density of galactic material.” The comparison value is Oort's 1958 star-count estimate, with no nucleosynthesis in it. The parameter h was lowered to fix deuterium and helium-3, not helium-4. The modern Planck baryon density is about 4 × 10⁻³¹ g/cm³. ↩
3. 46c.
  Page 24: Their best-fit comparison table gives computed He⁴ 0.25 against solar-system 0.27, and computed Li⁷ 3 × 10⁻¹⁰ against an observed 10⁻⁸. The lithium-7 figure is an under-prediction by a factor of about 33, the opposite sign to the modern lithium problem. Section Introduction: Their introduction also records the honest sentence: “Peebles (1966a, b) has reconsidered the Friedmann case with a view to obtaining the solar helium value.” ↩
47.
Pitrou, Cyril et al. “Precision big bang nucleosynthesis with improved helium-4 predictions.” Physics Reports 754:1–66. 2018. A theory paper that recalculates how much helium-4 the early universe should have made, adding a set of small physics corrections that the authors say are all included together for the first time. Its predicted helium-4 share of the ordinary matter, a mass fraction, is 0.24709 ± 0.00017. The article uses it for the claim that once the number of neutrino families and the baryon density are fixed, this model has no free parameter left. Mirror: arXiv
1. 47a.
  From the abstract. “Now that the number of neutrino families and the baryonic densities have been fixed by laboratory measurements or CMB observations, the model has no free parameter and its predictions are rigid.” Their conclusion on lithium: “Our predicted lithium abundance remains a factor of ≈3 above the Spite plateau. The solution of this problem probably involves several mechanisms including stellar depletion and possibly some physics beyond the standard model.” ↩
48.
Launders et al. arXiv:2604.16600. 2026. A 2026 preprint by Launders, Giovanetti and Liu, and a second 2026 preprint by Poulin, Froustey, Pitrou and Smith (arXiv:2607.20635), both report a growing deuterium tension of about 2σ, and the second proposes a transient scalar field during nucleosynthesis to absorb it. Launders' Table II shows that the whole range from 0.06σ agreement to 1.74σ tension comes from how the d(d,n)³He and d(d,p)³H cross sections are fitted, which the article uses for the caveat that a competing treatment pushes the comparison out to about 2σ. For scale only, the three leading CMB experiments give 100 Ω_b h² = 2.221 (SPT-3G), 2.238 (Planck) and 2.257 (ACT). ↩
49.
Fields, B. D. et al. “Big-Bang Nucleosynthesis.” Review of Particle Physics, Particle Data Group. Aug 2025. A review, revised in August 2025, in the Particle Data Group's Review of Particle Physics. It covers Big-Bang nucleosynthesis, the making of the lightest elements in the first few minutes of the universe. The article uses it for the review's statement that helium-3 is not a usable test of the Big Bang.
1. 49a.
  On helium-3, the review states that it is. “inappropriate to use ³He (and also D+³He) as a cosmological probe”. because stars both create and destroy it, and the only data come from the solar system and the solar-metallicity Milky Way. ↩
50.
Fixsen, D. J. “The Temperature of the Cosmic Microwave Background.” Astrophysical Journal 707:916–920. 2009. A short paper that recalibrates the FIRAS data against the WMAP satellite's data and then combines the result with earlier temperature measurements. It arrives at 2.72548 ± 0.00057 K for the background's temperature. The article uses it for that temperature and for the spread of the measurements behind it. Mirror: arXiv
1. 50a.
  Section Abstract: “The determination from the measurements from the literature is cosmic microwave background temperature of 2.72548 ± 0.00057 K.” It is a weighted mean of fifteen independent measurements selected by an uncertainty cutoff of 50 mK: CN-molecule excitation, balloon, rocket, South Pole, ARCADE 1 and 2, and three FIRAS analyses. ↩
51.
Chluba, J., and R. A. Sunyaev. “Superposition of blackbodies and the dipole anisotropy: A possibility to calibrate CMB experiments.” Astronomy & Astrophysics 424:389–408. 2004. A theory paper that asks what happens when many blackbodies at different temperatures are added together, using the temperature ripples in the CMB measured by COBE and WMAP. It finds that the sum is not a blackbody and leaves a y-type spectral distortion, a specific change in the shape of the spectrum. The article uses it for the claim that ordinary sources cannot add up to a perfect blackbody.
1. 51a.
  Section Abstract: “These distortions are connected with the simple fact, that the superposition of blackbodies with different temperatures in general is not a blackbody. We show, that in the limit of small temperature fluctuations, the superposition of blackbodies leads to a y-type spectral distortion.” Section 1: “These distortions are inevitable when the CMB is observed with finite angular resolution or when regions on the sky containing blackbodies with different temperatures are compared with each other.” ↩
52.
Chluba, J., and R. A. Sunyaev. “The evolution of CMB spectral distortions in the early Universe.” Monthly Notices of the Royal Astronomical Society 419:1294–1314. 2012. A theory paper that recomputes how energy released in the early universe would leave a mark on the shape of the CMB spectrum, using a new computer code called CosmoTherm. It concludes that the proposed Pixie experiment could improve some existing limits, while several other kinds of distortion would stay too small to see. The article uses it for the redshift at which the window for making photons closes.
1. 52a.
  Section 1: “For very early energy release (z ≳ 2 × 10⁶), photon production at low frequencies by double Compton emission and the up-scattering of photons to high frequencies by Compton scattering are so efficient that the thermalization process is practically perfect… However, below this redshift the CMB spectrum becomes vulnerable, and spectral distortions that could still be observable today can form.” Section 2.1: “To thermalize spectral distortions… (i) the number of photons has to be readjusted and (ii) photons have to be redistributed over frequency.” ↩
53.
Li, Aigen. “Cosmic Needles versus Cosmic Microwave Background Radiation.” Astrophysical Journal 584:593–598. 2003. A 2003 paper in the Astrophysical Journal by a theoretical astrophysicist at the University of Arizona, testing the proposal that radiation from early objects was thermalized into the microwave background by conducting needles of iron dust. The article uses it because it rules out two of the three ways of calculating that heating and leaves the third standing but unjustified.
1. 53a.
  Abstract: “We show here that the Rayleigh approximation is not valid… We also show that the available intergalactic iron dust, if modelled as infinite cylinders, is not sufficient to supply the required opacity at long wavelengths to obtain the observed isotropy and Planckian nature of the CMB. If appealing to the antenna theory, conducting iron needles with exceedingly large elongations (> 10⁴) appear able to provide sufficient opacity to thermalize the CMB within the iron density limit. But the applicability of the antenna theory to exceedingly thin needles of nanometer/micrometer in thickness needs to be justified.” Two of the three calculational routes are killed; the third survives but is unvalidated. ↩
54.
Lieu, Richard, and Jonathan P. D. Mittaz. “On the Absence of Gravitational Lensing of the Cosmic Microwave Background.” Astrophysical Journal 628:583–593. 2005. A 2005 paper by two physicists at the University of Alabama in Huntsville, which calculates how mass clumps along the line of sight would lens the microwave background and argues that WMAP's data rule out the size of effect it predicts. The article uses it because the paper's own conclusion is about the geometry of space, not about the background being local.
1. 54a.
  Section §11: “We therefore end with the startling conclusion that the large scale curvature of space may not entirely be an initial value problem related to inflation. The absence of gravitational lensing of the CMB point to the possibility that even effects on light caused by wrinkles in the space of the late (nearby) Universe have been compensated for, beyond some distance scale, by a mechanism which maintains a flat geometry over such scales.” The paper claims a dispersion in acoustic-peak angular size, not a null lensing detection, and states no significance level for its central claim. Their abstract calls the cluster case the robust one "because their properties are well understood." ↩
55.
Lewis, Antony, and Anthony Challinor. “Weak gravitational lensing of the CMB.” Physics Reports 429:1–65. 2006. A review of the subject by two cosmologists at Cambridge, covering how gravitational lensing changes the microwave background, its power spectra and the cosmological parameters that can be drawn from it. It was posted six months after Lieu and Mittaz appeared in ApJ, and it is the standard review of the subject. The article uses it as the rebuttal of Lieu and Mittaz, printed within six months.
1. 55a.
  Page 11: Footnote 5: “Ref. (37) claims a several-percent effect on the main CMB acoustic peaks; this is incorrect because the scale dependence and correlation of the magnification were not properly accounted for.” Section Footnote 4 of the companion Lieu & Mittaz paper (ApJ 623:L1): reads simply: “The contrary claim in Ref. (31) is erroneous.” ↩
2. 55b.
  Section §1.5: “On arcminute scales the CMB is very smooth due to diffusion damping. Magnification of a smooth surface does not change what you see at all… To have an interesting effect we need arcminute-scale coherent magnification, corresponding to arcminute scale deflection angles. This is much larger than the amount of deflection produced by most of the structures giving rise to large magnifications.” ↩
56.
Planck Collaboration. “Planck 2018 results. VIII. Gravitational lensing.” Astronomy & Astrophysics 641:A8. 2020. A Planck team paper that measures gravitational lensing of the microwave background, the bending of its light by the mass between us and it, using the final 2018 temperature and polarization data. Its headline result is lensing detected at 40σ, and it shows that the bending can be removed to sharpen the acoustic peaks. The article uses it for both points. Mirror: arXiv
1. 56a.
  From the abstract. “we increase the significance of the detection of lensing in the polarization maps from 5σ to 9σ. Combined with temperature, lensing is detected at 40σ.” ↩
2. 56b.
  Section 1: “we demonstrate that the CMB acoustic peaks can be delensed, detecting peak sharpening at 11σ from the Planck reconstruction alone and 15σ on further combining with the CIB… We also detect at 9σ a decrease in power of the B-mode polarization after delensing.” The paper contains a subsection titled "Acoustic peak sharpening (de-smoothing)." ↩
57.
Raghunathan, S. et al. “Detection of CMB-Cluster Lensing using Polarization Data from SPTpol.” Physical Review Letters 123:181301. 2019. A Physical Review Letters paper that detects gravitational lensing of the microwave background by individual galaxy clusters, using polarization data from the SPTpol telescope. It reports the lensing at 4.8σ. The article uses it as one of the three telescopes it cites for lensing by single clusters. Mirror: arXiv
1. 57a.
  From the abstract. “we detect lensing at 4.8σ. The mean stacked mass of the selected sample is found to be (1.43 ± 0.4) × 10¹⁴ M_☉ which is in good agreement with optical weak lensing based estimates using DES data and CMB-lensing based estimates using SPTpol temperature data.” Earlier cluster-lensing detections: Madhavacheril et al., PRL 114 (2015): 151302 (ACTPol, 3.2σ); Baxter et al., ApJ 806 (2015): 247 (SPT, 3.1σ). ↩
58.
Planck Collaboration. “Planck 2015 results. XXVII. The second Planck catalogue of Sunyaev-Zeldovich sources.” Astronomy & Astrophysics 594:A27. 2016. A Planck team catalogue of galaxy clusters found through the Sunyaev-Zeldovich effect, the small shift in the background caused by hot gas in a cluster, using 29 months of full-mission data. The article uses its all-sky count of 1,653 detections, of which 1,203 are confirmed. Mirror: arXiv
1. 58a.
  From the abstract. “It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data-sets, and is the first SZ-selected cluster survey containing > 10³ confirmed clusters.” A 2026 Planck meta-catalogue (arXiv:2606.17626) lists 1,962 entries and 1,500 confirmed clusters. SPT-SZ over 2500 deg² confirmed 516 of 677 candidates (Bleem et al., ApJS 216:27, 2015). ↩
59.
Hincks, A. D. et al. arXiv:1803.03277. Mar 12, 2019. The arXiv comment on that version reads: “Problem with MCMC convergence discovered during review process, resulting in significantly altered results indicating poorly understood systematics; if future investigation can control systematics a new paper will be submitted.” A preprint by four authors that claimed a detection of a relativistic refinement of the Sunyaev-Zel'dovich effect, the change in microwave light that hot gas in galaxy clusters causes, at about 5σ. The authors withdrew it after a review found a problem that changed the results significantly. The date is that of the second version, the one that carries the withdrawal. The current measurement that replaces it is Erler, Basu, Chluba and Bertoldi, MNRAS 476 (2018): 3360, at 2.0-2.2σ. The article warns against citing the withdrawn number. ↩
60.
Planck 2018 acoustic peak and trough positions. 2018. The measured positions in the Planck 2018 data: polarization (EE) peaks at multipoles 398.3, 690.4, 993.1 and 1296.4; temperature (TT) troughs at 416.3, 675.5, 1001.1 and 1290.0. An adiabatic acoustic mode requires the polarization peaks to fall on the temperature troughs, which was stated in advance in the introduction to the paper that first detected E-mode polarization (Kovac et al., Nature 420:772, 2002). The article uses it as a prediction with no adjustable freedom, which a reader can check against the two tables. ↩
61.
Eddington, A. S. The Internal Constitution of the Stars. Pages 371–372. Cambridge University Press. 1926. A book on the physics of stars by Sir A. S. Eddington. Its Chapter XIII, §256, "The Temperature of Space," works out the temperature that starlight would give a black body. The article uses it for Eddington's own calculation of that temperature, 3°·18, and for his statement that radiation in interstellar space is far from thermodynamic equilibrium.
1. 61a.
  Page 371: The paragraph comes straight after the 3°·18 calculation. “It is possible, however, for matter which has strong selective absorption to rise to very much higher temperature… Radiation in interstellar space is about as far from thermodynamical equilibrium as it is possible to imagine, and although its density corresponds to 3°·18 it is much richer in high-frequency constituents than equilibrium radiation of that temperature.” ↩
2. 61b.
  Table 48, page 372: "Equivalent Temperatures of Radiation in Space": λ = 6000 Å → 690 K; 4000 Å → 967 K; 2000 Å → 1750 K; 600 Å → 4707 K. ↩
62.
McKellar, A. “Molecular Lines from the Lowest States of Diatomic Molecules Composed of Atoms Probably Present in Interstellar Space.” Publications of the Dominion Astrophysical Observatory, Victoria 7(15):251–272. 1941. A longer paper by McKellar from the Dominion Astrophysical Observatory in Victoria, B.C. It reports sharp lines of CH and CN that W. S. Adams had detected in an early class B star, and it gives laboratory wavelengths for more than twenty-five common diatomic molecules. From the CN lines it derives a "rotational" temperature of 2.3 K for the region where the absorption takes place. The article uses it for that 2.3 K value and for McKellar's own description of it as the excitation temperature of interstellar cyanogen.
1. 62a.
  Page 268: “Thus from (3) we find, for the region of space where the CN absorption takes place, the 'rotational' temperature, T = 2°·3 K.” ↩
2. 62b.
  Page 268: “since we have only two lines of the R branch of the λ3883 CN band available, a thermal distribution cannot be demonstrated but must be assumed in order to evaluate T from equation (3).” Page 267: On Eddington's number. “Radiation in interstellar space, being the integrated total radiation from many sources of different temperatures and intensities, certainly does not correspond to a Planckian distribution for any one temperature.” ↩
63.
McKellar, A. “Evidence for the Molecular Origin of Some Hitherto Unidentified Interstellar Lines.” Publications of the Astronomical Society of the Pacific 52:187–192. 1940. A short 1940 paper that matches three unidentified sharp absorption lines from interstellar space to lines of the molecules CH, NaH and CN. It argues that almost all of those molecules would sit in their lowest rotational level, so only those lines would be strong enough to see. The article uses it for McKellar's own doubt about whether a temperature has any meaning in gas that thin, and for the upper limits his line ratio gives.
1. 63a.
  Page 192: “the 'effective' or 'rotational' temperature of interstellar space must be extremely low if, indeed, the concept of such a temperature in a region with so low a density of both matter and radiation has any meaning… if R(1) is not more than one-third, one-fifth, or one-twentieth as intense as R(0), the maximum 'effective' temperature of interstellar space would be 2.7° K, 2.1° K, and 0.8° K, respectively.” ↩
64.
Kragh, Helge. Cosmology and Controversy: The Historical Development of Two Theories of the Universe. Princeton University Press. 1996. A history of how two theories of the universe developed and came into conflict, the big bang and the steady state. The article uses it for the cosmic temperatures that the big bang's authors published, for the Soviet and papal reactions to the theory, and for a warning from John Paul II against using the big bang as apologetics.
1. 64a.
  Pages 132–134: Kragh's ledger of published temperature predictions. Alpher and Herman gave 5 K in 1948 and 1949, and 28 K in 1950, because they adopted Alfred Behr's density estimate of 10⁻²⁹ g/cm³, ten times the one used earlier. Gamow's 1950 figure of 3 K came with no derivation: “without any argument at all”. Gamow's 50 K, from The Creation of the Universe, was obtained. “by simply inserting the age of the universe… in the equation… This is obviously not valid since the relationship only holds in the early, radiation-dominated period”. Gamow gave 7 K in 1953 and 6 K in 1956. ↩
2. 64b.
  Page 134: “even if the prediction was understood, it may have seemed of theoretical interest only; neither Gamow, Alpher, nor Herman suggested that it might actually be detected, and if so, how.” Page 133: “The prediction of the cosmic background radiation was first made in 1948 and it was repeated at least seven times until 1956. It was thus well known, but made no impact at all.” ↩
3. 64c.
  Page 262: Quoting Andrei Zhdanov in 1947: “The reactionary scientists Lemaitre, Milne and others made use of the 'red shift' in order to strengthen religious views on the structure of the universe… Falsifiers of science want to revive the fairy tale of the origin of the world from nothing.” ↩
4. 64d.
  Page 257: The peroration of Pius XII's address Un'Ora to the Pontifical Academy of Sciences, 22 November 1951, as Kragh quotes it: “Thus, with that concreteness which is characteristic of physical proofs, it has confirmed the contingency of the universe and also the well-founded deduction as to the epoch when the world came forth from the hands of the Creator. Hence, creation took place. We say: therefore, there is a Creator. Therefore, God exists!” The Italian original is in Acta Apostolicae Sedis 44 (1952): 31–43. Pius XII attached his own hedge in the next clause, “benché non esplicita né compiuta”. which the standard English rendering drops. ↩
5. 64e.
  Page 258: “Lemaitre, whose theory of the primeval universe formed the backbone of the pope's argument, was not at all happy with the address. Himself a Catholic priest and high-ranking member of the Pontifical Academy, Lemaitre believed that astronomy and theology were two separate contexts which should not be mixed; He also felt that the big-bang theory was still a hypothesis, and that the pope had presented it in a much too authoritative way. He was therefore quite upset and found it necessary to intervene, together with Daniel O'Connell, the director of the Vatican Observatory and science adviser to the pope.” Kragh adds his own hedge, which travels with the quotation: “Apparently they succeeded.” ↩
6. 64f.
  Page 258: “Never again did Pope Pius XII try to make cosmology support Christian dogma.” ↩
7. 64g.
  Page 259: John Paul II's message of 1 June 1988, as Kragh quotes it: “Christianity possesses the source of its justification within itself and does not expect science to constitute its primary apologetic”. , with a specific warning against. “making uncritical and overhasty use for apologetic purposes of such recent theories as that of the 'Big Bang' in cosmology.” ↩
65.
Dicke, R. H. et al. “Cosmic Black-Body Radiation.” Astrophysical Journal 142:414–419. 1965. A short letter to the editor by four physicists. It argues that the early universe may have been hot enough for its radiation to be a black body, that this radiation should still be detectable, and it describes a radiometer the authors were building to look for it, which had not yet produced results. The article uses it for the claim that the 40 K prediction was not a prediction, because the letter gives its temperature only as a rough upper limit.
1. 65a.
  Page 415: “Without some knowledge of the density of matter in the primordial fireball we cannot predict the present radiation temperature. However, a rough upper limit is provided by the observation that black-body radiation at a temperature of 40° K provides an energy density of 2 × 10⁻²⁹ gm cm⁻³, very roughly the maximum total energy density compatible with the observed Hubble constant and acceleration parameter.” The companion paper (Penzias & Wilson, ApJ 142:419) reported 3.5° ± 1° K. ↩
66.
Hoyle, Fred. Home Is Where the Wind Blows: Chapters from a Cosmologist's Life. University Science Books (Mill Valley, CA). 1994. An autobiography by Fred Hoyle, who with Hermann Bondi and Tommy Gold began work on the rival idea of continuous creation of matter in 1946 and 1947. In its last chapter he claims a substantial role in the rise of big-bang cosmology in the 1960s and argues that the theory has delivered little success for a great deal of effort. He is a partisan of the rival steady-state theory, so his verdicts are opinions, not findings. The article uses it for his two sharpest objections to the big bang.
1. 66a.
  Page 413: “Big-bang cosmology is a form of religious fundamentalism, as is the furor over black holes, and this is why these peculiar states of mind have flourished so strongly over the past quarter century.” Page 407: “Much as I have always disliked the big bang…” ↩
2. 66b.
  Page 413: “How, in big-bang cosmology, is the microwave background explained? Despite what supporters of big-bang cosmology claim, it is not explained… Had observation given 27 kelvins instead of 2.7 kelvins for the temperature, then 27 kelvins would have been entered in the catalogue. Or 0.27 kelvin. Or anything at all.” ↩
67.
Eisenstein, Daniel J. et al. “Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies.” Astrophysical Journal 633:560. 2005. A measurement of how 46,748 luminous red galaxies from the Sloan Digital Sky Survey are spread across 3816 square degrees of sky. It finds the sound-wave pattern from the early universe in that spread, at 100 h^-1 Mpc separation, and reports that it matches the prediction from the microwave background. The article uses it as the detection of this pattern in galaxy clustering, a result the 2dF survey also found that same year. Mirror: arXiv
1. 67a.
  Section Abstract: “We find a well-detected peak in the correlation function at 100h⁻¹ Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z ≈ 1000 and the present and confirms a firm prediction of the standard cosmological theory.” ↩
2. 67b.
  Section §4.2: “The baryon signature is therefore detected at 3.4 σ.” “no information from the CMB on Ω_m h² has been used in computing χ², and so our constraint on Ω_m h² is separate from that from the CMB.” ↩
68.
Cole, Shaun et al. “The 2dF Galaxy Redshift Survey: power-spectrum analysis of the final data set and cosmological implications.” Monthly Notices of the Royal Astronomical Society 362:505. 2005. A statistical analysis of the final 2dF Galaxy Redshift Survey, which measured the redshifts of 221,414 galaxies, to see how galaxies are spread across the sky on large scales. The paper is by the 2dFGRS Team. The article uses it to show that the survey's own authors tie their result to the standard model of cosmology.
1. 68a.
  Section 7: “It should be emphasised that the above statements depend on the theoretical framework of the ΛCDM model… What is impressive in our data is not simply that the results suggest departures from a smooth curve, but that these deviations occur in the locations expected from theory. It is this prior knowledge that gives the extra statistical power needed in order to reject a zero-baryon model with confidence.” They rate their own detection at. “about the 1% level”. , and say the apparent 4σ. “overstates the significance.” ↩
69.
Giannantonio, Tommaso et al. “The significance of the integrated Sachs-Wolfe effect revisited.” Monthly Notices of the Royal Astronomical Society 426:2581. 2012. A data analysis by four astronomers that updates the measurement of the integrated Sachs-Wolfe effect, a faint extra pattern in the cosmic background that appears when dark energy begins to dominate the expansion. It uses the seven-year WMAP maps and newer Sloan Digital Sky Survey galaxy data, combines them into one detection strength, and tests for systematic errors that critics had raised, including a rotation test. The article uses its 4.4 sigma figure as the strength of this detection. Mirror: arXiv
1. 69a.
  Section Abstract: “we now obtain a combined significance of the ISW detection at the 4.4 σ level, which fluctuates by ~0.4σ when alternative data cuts and analysis assumptions are considered.” Planck 2015 XXI gets 4σ from the joint cross-correlation. ↩
70.
Planck Collaboration. “Planck 2015 results. XXI. The integrated Sachs-Wolfe effect.” Astronomy & Astrophysics 594:A21. 2016. A Planck team paper on the integrated Sachs-Wolfe effect, a faint extra signal in the background caused by gravitational wells that change over time. The authors correlate the background with galaxy and radio catalogues and with Planck's own lensing map. They detect the effect at 4σ when all the data are combined, but only at about 3σ from Planck's data alone, so the article uses it for that weakness and for the anomalous signal the paper reports around superclusters and supervoids. Mirror: arXiv
1. 70a.
  From the abstract. “we show that Ω_Λ is detected at more than 3 σ.” The anomaly the article does not omit: “the Planck polarization data are used to study the anomalously large ISW signal previously reported through the aperture photometry on stacked CMB features at the locations of known superclusters and supervoids, which is in conflict with ΛCDM expectations. We find that the current Planck polarization data do not exclude that this signal could be caused by the ISW effect.” ↩
71.
Atek, Hakim et al. “Most of the photons that reionized the Universe came from dwarf galaxies.” Nature 626:975–978. 2024. A research article reporting observations of eight ultra-faint galaxies in a very small field, during the first billion years of the universe. The authors add a condition: their result holds only if that small field is representative of faint galaxies generally. The article uses it for the claim that these galaxies make four times the ionizing light that models assumed.
1. 71a.
  Section Abstract: “We find that faint galaxies during the Universe's first billion years produce ionizing photons with log(ξ_ion / Hz erg⁻¹) = 25.80 ± 0.14, a factor of 4 higher than commonly assumed values. If this field is representative of the large scale distribution of faint galaxies, the rate of ionizing photons exceeds that needed for reionization, even for escape fractions of order five per cent.” ↩
72.
Muñoz, Julian B. et al. “Reionization after JWST: a photon budget crisis?” Monthly Notices of the Royal Astronomical Society: Letters 535:L37. 2024. A short theory paper that tests whether the galaxies seen by the James Webb Space Telescope can have finished reionization, the period when hydrogen between galaxies went from neutral to ionized. It counts the ionizing photons that the observed galaxies would produce and let escape. It finds that they make too many photons, so reionization would end too early. The article uses it to show that the live problem now runs the other way, with too many photons rather than too few.
1. 72a.
  Section Abstract: “we show that the galaxies we have directly observed (M_UV < −15) not only can drive reionization, but would end it too early. That is, our current galaxy observations, taken at face value, imply an excess of ionizing photons and thus a process of reionization in tension with the cosmic microwave background (CMB) and Lyman-α forest.” The authors name the possible ways out: “systematics in either theory or observations”. ↩
73.
Valcin, David et al. “The Age of the Universe with Globular Clusters: Reducing Systematic Uncertainties.” Journal of Cosmology and Astroparticle Physics (08):017. 2021. A 2021 paper that estimates the age of the universe from globular clusters, the oldest star clusters, and tries to shrink the systematic errors in that method. The article uses it for an age of 13.5 billion years and a systematic error of 0.23 to 0.33 billion years. Mirror: arXiv
1. 73a.
  “This results in an age of the Universe tU = 13.5^+0.16−0.14_ (stat.) ± 0.23(0.33) (sys.) at 68% confidence level, accounting for the formation time of globular clusters and its uncertainty.” Their 2020 paper (JCAP 12:002) gives the underlying cluster age as 13.32 ± 0.1 (stat) ± 0.5 (sys) Gyr from 68 clusters, and describes it as. “largely independently of the cosmological parameters.” Jimenez et al. (JCAP 03 (2019): 043) turn stellar ages alone into H₀ = 69-71 km/s/Mpc, with no early-universe physics. ↩
74.
Ying, Jiaqi M. et al. “The Absolute Age of M92.” The Astronomical Journal 166:18. 2023. A research paper that dates the star cluster M92 by building 20,000 sets of theoretical isochrones (computer models of stars that all share one age), with the physics inputs varied at random. It finds an age of 13.80 ± 0.75 Gyr (billion years), and the uncertainty in the distance to the cluster is about 80% of the error budget. The article uses it as a 2023 example of dating old star clusters, set beside a 2021 analysis of 68 clusters. Mirror: arXiv
1. 74a.
  Section Abstract: “we construct 20,000 sets of theoretical isochrones through Monte Carlo simulation… we vary a range of input physics used in the stellar evolution models, including opacities, nuclear reaction rates, diffusion coefficients, atmospheric boundary conditions, helium abundance, and treatment of convection… We find the age of M92 to be 13.80 ± 0.75 Gyr. The 5.4% error in the absolute age is dominated by the uncertainty in the distance to M92 (~80% of the error budget).” The method assumes stellar physics and a distance scale. It assumes nothing cosmological. ↩
75.
Bedin, L. R. et al. “The HST Large Programme on NGC 6752. III. Detection of the Peak of the White Dwarf Luminosity Function.” MNRAS 488:3857. 2019. Part III of a Hubble Space Telescope programme on the star cluster NGC 6752, reporting a white-dwarf cooling age of about 14 billion years (Gyr). The article uses it for the agreement between the cooling clock and the turnoff clock in that cluster.
1. 75a.
  Section Abstract: “we have reached the peak of the luminosity function of the WD cooling sequence, at a magnitude m_F606W = 29.4 ± 0.1, which is consistent with a formal age of ~14 Gyr. This age is also consistent with the age from fits to the main-sequence turnoff (13-14 Gyr).” ↩
76.
Kilic, Mukremin et al. “The Age of the Galactic Stellar Halo from Gaia White Dwarfs.” Monthly Notices of the Royal Astronomical Society 482:965. 2019. A study that dates the galactic stellar halo by measuring how far its white dwarfs have cooled, using Gaia white dwarf candidates. The article uses it for the one halo white dwarf whose cooling age, 10.3 Gyr, sets a floor on the age of the inner halo.
1. 76a.
  Section Abstract: “The white dwarf cooling ages of our targets range from 7 Myr for J1657+2056 to 10.3 Gyr for J1049-7400. The latter provides a firm lower limit of 10.3 Gyr for the age of the inner halo based on the well-understood physics of white dwarfs.” ↩
77.
Cayrel, R. et al. “Measurement of stellar age from uranium decay.” Nature 409:691. 2001. A short research letter that measures the uranium in a star and turns that measurement into an age. The authors' abstract gives the age as 12.5 ± 3 billion years and says it is still model dependent. The article uses it because it was the first uranium detection in a star, and it gave an age.
1. 77a.
  Section Abstract: “The derived uranium abundance, log(U/H) = −13.7 ± 0.14 ± 0.12 yields an age of 12.5 ± 3 Gyr, though this is still model dependent.” ↩
78.
Toenjes, R. et al. “Tuning the Clock: Uranium and Thorium Chronometers Applied to CS 31082-001.” Astrophysical Journal 579:626. 2002. A paper that dates one very old star, CS 31082-001, with uranium and thorium clocks, and shows how its age depends on the nuclear mass model chosen. The article uses it to show that this method needs a theoretical production ratio that is not well known, so the same star can come out five billion years apart. Mirror: arXiv
1. 78a.
  “The [U/Th] ratio yields an age of 13 ± 4 Gyr or 8 ± 4 Gyr, based on the use of the ETFSI-Q or the new HFBCS-1 nuclear mass models, respectively.” Same star, same measured abundances, five billion years apart. ↩
79.
Shah, Shivani P. et al. “Uranium Abundances and Ages of R-process Enhanced Stars with Novel U II Lines.” Astrophysical Journal 948:122. 2023. A 2023 study that measured uranium in four very old stars, using two new uranium spectral lines beside the usual one, and then dated those stars with radioactive clocks. It found that the new lines give uranium amounts that agree with the old line. The article uses it for the size of the uncertainty in radioactive-clock ages and for the wide, partly negative range of ages that the thorium/europium clock has produced. Mirror: arXiv
1. 79a.
  Section 7: “The resulting total uncertainties on the ages of the sample stars are on the order of ~4 - 6 Gyr for the U/Th ages and ~3 - 4 Gyr for the U/Eu ages.” Section 1: On the production-ratio problem: “the application of the Th/Eu chronometer to RPE stars has led to a large range in ages from 21 Gyr to −9 Gyr, even though these stars are metal-poor,”. About 30% of r-process-enhanced stars give negative ages. ↩
80.
Guillaume, C. et al. “The age of the Methuselah star in light of stellar evolution models with tailored abundances.” Astronomy & Astrophysics 692:L3. 2024. A 2024 paper on the age of HD 140283, the star nicknamed Methuselah, using stellar evolution models built with tailored element abundances. Its tailored models give an age of 12.3 billion years, while a standard solar mixture gives 14 billion years. The article cites it as one of six published ages for the star. Mirror: arXiv
1. 80a.
  Section Abstract: “With our tailored models we find an age of 12.3 Gy. Using a solar-scaled mixture instead results in an age value of 14 Gy, in tension with the age of the universe (13.77 ± 0.06 Gy).” A 1.7-Gyr swing from one modelling choice. ↩
81.
Lundkvist, M. S. et al. “Asteroseismic investigation of HD 140283: The Methuselah star.” Astronomy & Astrophysics 703:A232. 2025. A 2025 study of HD 140283, nicknamed Methuselah, that reads the star's interior from its oscillations, a method called asteroseismology. It gives the star a mass of 0.75 solar masses and an age of 14.2 ± 0.4 billion years (Gyr). The article uses it as the newest age for the star, and the paper itself warns that its quoted error bars leave out systematic effects.
1. 81a.
  Section Abstract: “an age of 14.2 ± 0.4 Gyr, in agreement with the upper limit set by the age of the Universe within 1σ.” Other published ages for the same star: 14.46 ± 0.31 (Bond 2013), 14.27 ± 0.38 (VandenBerg 2014), 12.01 ± 0.05 (Tang & Joyce 2021), 12.3 or 14 (Guillaume 2024, depending on the opacity table), 13.5 ± 0.7 (Jimenez 2019, post-Gaia). Section 6.1: “the uncertainties are those quoted by BASTA, not accounting for all systematic effects… realistic age uncertainties for sub-giants are higher, for HD 140283 perhaps of the order of 10%”. That is, ±1.4 Gyr, not ±0.4. ↩
82.
Bond, Howard E. et al. “HD 140283: A Star in the Solar Neighborhood that Formed Shortly After the Big Bang.” Astrophysical Journal Letters 765:L12. 2013. A short research letter that uses a precise distance to the star to infer its age, which it gives as 14.46 billion years. The article uses it because the authors' own abstract says the age does not conflict with the age of the universe.
1. 82a.
  Section Abstract: “we use the precise distance to infer an age of 14.46 +/- 0.31 Gyr. The quoted error includes only the uncertainty in the parallax… Uncertainties in the stellar parameters and chemical composition, especially the oxygen content, now contribute more to the error budget for the age of HD 140283 than does its distance, increasing the total uncertainty to about +/-0.8 Gyr. Within the errors, the age of HD 140283 does not conflict with the age of the Universe, 13.77 +/- 0.06 Gyr.” VandenBerg et al., ApJ 792 (2014): 110, put the excess at "< 1σ." ↩
83.
Krauss, Lawrence M., and Michael S. Turner. “The Cosmological Constant Is Back.” General Relativity and Gravitation 27:1137. 1995. A short essay, written for a 1995 essay competition, by two physicists who argue that several kinds of observation now call for a nonzero cosmological constant. The article uses it for the age problem: with a Hubble constant of 80 km/s per megaparsec, the expansion age comes out shorter than the age of the oldest globular clusters.
1. 83a.
  Pages 2–3: “The expansion age for a Hubble constant of 80 km s⁻¹ Mpc⁻¹ is 8.2 Gyr for the theoretically favored flat Universe. Even taking a conservative lower bound to the fraction of critical density in matter… leads to an expansion age of only 10.4 Gyr. Therein lies the problem; the ages of the oldest globular clusters are estimated to be 16 ± 3 Gyr, and it is likely that a Gyr or so elapsed before the formation of these stars… The age problem is more acute than ever before.” ↩
84.
Chaboyer, Brian et al. “The Age of Globular Clusters in Light of Hipparcos: Resolving the Age Problem?” Astrophysical Journal 494:96. 1998. A study that re-measures how far away the oldest star clusters in our galaxy (globular clusters) are, using the Hipparcos satellite's parallax measurements and five independent distance techniques. It then re-estimates their ages with a Monte Carlo study, which is a computer simulation that runs many random trials. The article uses it as its example of a distance correction lowering an age estimate.
1. 84a.
  Section Abstract: “Our best estimate for the mean age of the oldest globular clusters is now 11.5 ± 1.3 Gyr, with a one-sided, 95% confidence level lower limit of 9.5 Gyr. This represents a systematic shift of over 2 σ compared to our earlier estimate, due completely to the new distance scale—which we emphasize is not just due to the Hipparcos data.” Their 1995/96 lower bound was 12.07 Gyr (Chaboyer, Kernan, Krauss & Demarque, Science 271:957). ↩
85.
Guth, Alan H. et al. “A Cosmic Controversy.” Scientific American. May 10, 2017. A letter to Scientific American signed by its four named authors and 29 co-signatories. Signatories include Stephen Hawking, Steven Weinberg, Edward Witten, Frank Wilczek, Martin Rees, Leonard Susskind, Juan Maldacena, Lisa Randall, Sean Carroll, Lawrence Krauss, George Efstathiou, Alexei Starobinsky, Alexander Vilenkin, George Smoot and John Mather. The article uses it for the letter's claim that inflation has passed its empirical tests.
1. 85a.
  “The average mass density of the universe has now been measured to an accuracy of about half of a percent, and it agrees perfectly with the prediction of inflation. (When inflation was first proposed, the average mass density was uncertain by at least a factor of three, so this is an impressive success.)” Also: “standard inflationary models could have failed any of the empirical tests described above, but they did not.” ↩
86.
Peiris, H. V. et al. “First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation.” Astrophysical Journal Supplement Series 148:213. 2003. A 2003 paper on what the first-year WMAP satellite data imply for inflation, the brief early expansion that is proposed to explain the large-scale smoothness of the universe. The article uses it for the large-angle temperature-polarization pattern, and for the paper's own hedge that other scenarios predict the same thing.
1. 86a.
  The temperature-polarization anticorrelation at large angles is evidence for super-horizon fluctuations, but the same paper hedges: “In addition to inflation, the pre-Big-Bang scenario and the Ekpyrotic scenario predict the existence of superhorizon fluctuations.” It confirms some epoch of accelerated expansion, not inflation uniquely. ↩
87.
Ijjas, Anna et al. “Inflationary paradigm in trouble after Planck2013.” Physics Letters B 723:261. 2013. A letter by three cosmologists that analyzes the inflation models which the 2013 Planck satellite data favor. It finds that the favored models make two old problems worse, the initial conditions problem and the multiverse problem, and create a third, which the authors call the "unlikeliness problem." It concludes that the data disfavor all the best-motivated inflation scenarios. The article uses it because one of the authors, Paul Steinhardt, helped build the theory, and because the authors say inflation now needs the smoothness it was meant to explain.
1. 87a.
  Section 2: “the universally accepted assumption about initial conditions no longer leads to inflation; instead, inflation can only begin to smooth the universe if the universe is unexpectedly smooth to begin with!” Section 3: “inflationary plateau-like models pass this test. However, this cannot be described as a success for the inflationary paradigm, since, according to inflationary reasoning, this particular class of models is highly unlikely to describe reality.” ↩
88.
Ijjas, Anna et al. “Pop Goes the Universe.” Scientific American. Feb 2017. A popular article in Scientific American by Anna Ijjas, Paul Steinhardt and Abraham Loeb, which argues that inflation would be unnecessary if a smooth, flat starting patch were easy to find. The article uses it for the charge that inflation is circular, since it needs the smooth starting conditions it was supposed to explain.
1. 88a.
  “if it were easy to find a patch emerging from the big bang that is flat and smooth enough to start inflation, then inflation would not be needed in the first place.” Also, the piece says inflation. “cannot be evaluated using the scientific method”. “no experiment can ever disprove it.” ↩
89.
Albrecht, Andreas. Cosmic Inflation and the Arrow of Time. 2002. A theoretical discussion of whether inflation can explain the arrow of time, not a measurement. It was written as a contribution to a 2003 Cambridge volume honouring John Wheeler's 90th birthday. Albrecht is one of inflation's co-founders, so the concession below comes from inside the theory. The article uses it for that concession.
1. 89a.
  “inflation does not predict the arrow of time. Inflation 'passes the arrow of time buck' to the special initial conditions of the inflaton field.” ↩
90.
Guth, Alan H. “Inflationary universe: A possible solution to the horizon and flatness problems.” Physical Review D 23:347. 1981. A 1981 paper in Physical Review D, first circulated as SLAC preprint SLAC-PUB-2576, that offers inflation as a possible answer to two puzzles about the early universe. The article uses it to show how modest the original proposal was.
1. 90a.
  The closing sentence: “I am publishing this paper in the hope that it will highlight the existence of these problems and encourage others to find some way to avoid the undesirable features of the inflationary scenario.” ↩
91.
Linde, Andrei. Inflationary Cosmology after Planck 2013. 2014. Section §11. A review of inflationary cosmology by Andrei Linde of Stanford University, based on lectures given at the Les Houches school in 2013, that assesses inflation in view of the Planck 2013 data. The article uses it for Linde's account of the models that were tried before dark energy was discovered.
1. 91a.
  “Before the discovery of dark energy, many astronomers believed that Ω ~ 0.3. At that time, experts in inflationary theory made many attempts to save inflation by inventing inflationary models compatible with this value of Ω, and none of these models worked except one of two models which were extremely artificial.” The models are real: Bucher, Goldhaber & Turok, "An open universe from inflation," Physical Review D 52 (1995): 3314; Linde & Mezhlumian, "Inflation with Ω ≠ 1," Physical Review D 52 (1995): 6789. Linde also concedes that the scale-invariance prediction predates inflation: Harrison-Zel'dovich is 1970. ↩
92.
Guth, Alan H. et al. “Inflationary paradigm after Planck 2013.” Physics Letters B 733:112. 2014. A 2014 paper by Alan Guth and two colleagues on the state of inflation after the Planck 2013 results. The article uses it as their reply to the charge that inflation is untestable, and for their own concession that some predictions are not tests of the paradigm.
1. 92a.
  The authors write: “we would view the success or failure of such predictions not as a test of the inflationary paradigm, but rather as part of our exploration of the measure problem.” They also concede that. “a persuasive theory of probabilities in the multiverse has not yet been found.” ↩
93.
Frenk, Carlos S., and Simon D. M. White. “Dark matter and cosmic structure.” Annalen der Physik 524:507–534. 2012. A review by Carlos Frenk of Durham and Simon White of the Max Planck Institute for Astrophysics, tracing how cosmic structure formed in the standard dark-matter model over forty years. It focuses on the role of computer simulations and on the nature of dark matter, and it gives a timeline of key developments. The article uses it for the authors' own admission that dark matter particles have not yet been found.
1. 93a.
  “even the most ardent supporters of the cold dark matter idea must remain sceptical until the dark matter particles are finally and conclusively discovered.” ↩
94.
Kim, Stacy Y. et al. “Missing Satellites Problem: Completeness Corrections to the Number of Satellite Galaxies in the Milky Way are Consistent with Cold Dark Matter Predictions.” Physical Review Letters 121:211302. 2018. A paper that corrects the count of the Milky Way's satellite galaxies for the faint ones that surveys cannot detect, and reports that the corrected count is consistent with cold dark matter predictions. The article uses it to show that the missing-satellites problem, once the standard list of dark matter's failures, is now closed on the count.
1. 94a.
  “The 'missing satellites problem', cast in terms of number counts, is thus solved.” ↩
95.
Sales, Laura V. et al. “Baryonic solutions and challenges for cosmological models of dwarf galaxies.” Nature Astronomy 6:897. 2022. A 2022 review by three researchers at UC Riverside, UC Davis and Durham University, which goes through the small-scale problems of the standard cosmological model, ΛCDM (dark energy plus cold dark matter), and rates how serious each one still is. The authors argue that simulations which include ordinary gas and stars have solved the missing-satellites problem, and they list the tensions that remain. The article uses it as a warning that apologetics still repeats a list of dark-matter failures that has mostly been closed.
1. 95a.
  This pro-ΛCDM review rates the missing-satellites problem solved, too-big-to-fail solved for satellites, and the core-cusp problem as. “uncertain”. , and the diversity of rotation curves as a. “strong tension”. . The 2017 Bullock & Boylan-Kolchin framing of a small-scale crisis no longer stands. ↩
96.
Bödeker, Dietrich, and Wilfried Buchmüller. “Baryogenesis from the weak scale to the grand unification scale.” Reviews of Modern Physics 93:035004. 2021. A review of the current status of baryogenesis, the processes that could produce the surplus of matter over antimatter, with its emphasis on electroweak baryogenesis and leptogenesis. The article uses it for the status of the matter-antimatter problem and of its proposed solutions.
1. 96a.
  Section §I, Eq. (1): “η_B ≡ n_B/n_γ = (6.12 ± 0.04) × 10⁻¹⁰,”. measured by Planck and. “consistent with the most recent analysis of primordial nucleosynthesis (except for the 'lithium problem').” Antimatter regions are excluded by the diffuse gamma-ray background. ↩
2. 96b.
  Section §II.A: The three Sakharov conditions: baryon-number violation; C and CP violation; departure from thermal equilibrium. The original is A. D. Sakharov, JETP Letters 5 (1967): 24. ↩
3. 96c.
  Section Summary: “The current paradigm of the early Universe includes inflation at an early stage. Hence, the observed matter-antimatter asymmetry cannot be imposed as an initial condition but it has to be dynamically generated after inflation. This makes baryogenesis an unavoidable topic.” ↩
4. 96d.
  “A baryon-to-photon ratio η_B ~ 10⁻⁹ then requires a heavy-neutrino mass M ≳ 10⁸ GeV and 10⁹ GeV for the two different initial conditions.” Section §III: “during the transition the system stays close to thermal equilibrium and Sakharov's third condition is not satisfied.” ↩
97.
Gavela, M. B. et al. “Standard Model CP-violation and Baryon asymmetry.” Modern Physics Letters A 9:795. 1994. A short paper by four physicists at CERN, Harvard, Heidelberg and Orsay, testing whether the known CP violation, a difference in behaviour between particles and their antiparticles, can explain the excess of matter over antimatter in the universe. It calculates the effect at zero temperature and in the hot plasma of the early universe, and finds it far too small. The article uses it as the theorists' own statement that known physics falls short of the matter asymmetry. Mirror: arXiv
1. 97a.
  Section Abstract: “The effect is many orders of magnitude below what observation requires, and indicates that non standard physics is indeed needed in the cosmological scenario.” Their computed asymmetries are 1.6 × 10⁻²¹ and −3 × 10⁻²⁴. They say. “the induced baryon asymmetry n_b/s cannot exceed 10⁻² times these results”. against an observed n_B/s of 4 to 6 × 10⁻¹¹. Huet and Sather, in Physical Review D 51:379, reached the same conclusion independently. ↩
98.
D'Onofrio, Michela, and Kari Rummukainen. “Standard model cross-over on the lattice.” Physical Review D 93:025003. 2016. A lattice study, meaning a computer calculation on a grid of points, of the Standard Model's symmetry-restoring transition at the physical Higgs mass. It finds the transition is a smooth crossover and measures the temperature at which it happens. The article uses it for the claim that the transition is a smooth crossover, so Sakharov's third condition for matter-antimatter asymmetry is not met. Mirror: arXiv
1. 98a.
  Section Abstract: “With the physical Higgs mass the Standard Model symmetry restoration phase transition is a smooth cross-over… We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result T_c = 159.5 ± 1.5 GeV.” ↩
99.
Lisle, Jason. A Big Bang. Biblical Science Institute. 2019. A three-part series by Jason Lisle, published on 5, 12 and 26 April 2019. The article quotes its argument from the matter-antimatter asymmetry, which it calls Lisle's strongest card.
1. 99a.
  Part 3: “if the big bang were true the universe should be 50% matter, and 50% antimatter. But in fact, the universe is essentially 100% matter. Therefore, we must conclude that the big bang is not true. Note that this conclusion is based on the observable, testable, repeatable results of laboratory physics.” Part 2 states the premise: “whenever energy becomes matter, it also produces an exactly equal amount of antimatter. There are no exceptions.” ↩
2. 99b.
  Part 3: “any universe with an average equilibrium temperature of 2.7 degrees will have a CMB. The expectation of a CMB is neither unique nor robust… In conclusion, the one successful prediction of the big bang wasn't really a prediction, was not specific, and is not uniquely explained by the big bang.” ↩
100.
Strassler, Matt. “Which Parts of the Big Bang Theory are Reliable, and Why?” Of Particular Significance (profmattstrassler.com). Mar 26, 2014. A blog post by Matt Strassler, a theoretical particle physicist (Rutgers, Harvard), who color-codes the history of the universe by how sure physicists can be. The piece's BICEP2 passages are stale, and he bracketed his own corrections into the live text. The article uses it for the point that claims about how the universe began are pure theory, not measured fact.
1. 100a.
  “So if people tells you that the universe started in such and such a way, perhaps 'with a singularity' or 'with a quantum fluctuation out of nothing' or 'in the Big Crunch (i.e. the collapse) of a previous phase of the universe', remember that they're telling you about the red zone. They're neglecting to tell you that what they're saying is pure theory, with neither an experiment to back it up nor a clear theoretical reason to believe their suggestion is unique and preferable over someone else's alternative.” His four zones run from nucleosynthesis onward. The green zone, where he says. “we have strong observational evidence that the Hot Big Bang did occur”. The yellow zone covers the electroweak era, which he calls. “a highly educated guess… though no direct experimental checks”. Inflation's late stages are orange, and everything earlier is red. His conclusion is. “the notion that the universe's heat and density increased to the extent that Einstein's equations have a singularity… is an assumption. So that part of the Big Bang Theory may not survive the test of time. You should be prepared, as scientists are, to let it go.” ↩
101.
Carroll, Sean M. Why Is There Something, Rather Than Nothing? 2018. An essay written as an invited contribution to the Routledge Companion to the Philosophy of Physics. It argues that the universe is unlikely to be the kind of thing that has a reason why it exists, using what modern physics and cosmology show about the laws of nature. The article uses it because Carroll says our incomplete understanding of quantum gravity fits both a universe that lasted forever and one with a first moment in time.
1. 101a.
  Page 6: “The best we can say is that our current incomplete understanding of quantum gravity is fully compatible with both the possibility that the universe has lasted forever, and that it had a first moment in time.” Page 8: “This is not to say that there is no Big Bang in the usual sense; only that it is not a true physical singularity as it would be in classical general relativity, nor does it represent the first moment of the universe.” ↩
102.
Senovilla, José M. M., and David Garfinkle. “The 1965 Penrose singularity theorem.” Classical and Quantum Gravity 32:124008. 2015. A historical review, by two physicists who study general relativity, of the 1965 theorem with which Roger Penrose proved the first modern singularity result. It covers the theorem's history, its impact and its later legacy. The article uses it for the authors' view that the singularity theorems are evidence that general relativity needs corrections in extreme gravity, rather than evidence of an actual infinite density. Mirror: arXiv
1. 102a.
  Page 16: Page numbers are those of the arXiv preprint. “Letting aside some subtleties, they are usually interpreted as providing evidence of the (classical) singular beginning of the Universe and of the singular final fate of massive compact stars. A more up-to-date perspective would rather state that they provide very solid evidence of the need of (possibly quantum) corrections to GR when extreme gravity effects occur.” Page 18: “(6) depends then on the sign of Λ and today we know that Λ > 0, just the wrong sign for the theorems… Actually, inflationary cosmological models violate it.” Both theorems conclude geodesic incompleteness, not infinite density. ↩
103.
Borde, Arvind et al. “Inflationary spacetimes are not past-complete.” Physical Review Letters 90:151301. 2003. A theoretical paper giving a simple argument, needing no energy condition, that an inflating universe must be incomplete in the past. The article uses it for the authors' conclusion that inflation alone does not describe the past boundary of the inflating region, so new physics is needed there.
1. 103a.
  Section Abstract: The abstract, in full: “Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating — or just expanding sufficiently fast — must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.” ↩
2. 103b.
  Section Conclusion, page 4: “it is clear that unless the averaged expansion condition can somehow be avoided for all past-directed geodesics, inflation alone is not sufficient to provide a complete description of the Universe, and some new physics is necessary in order to determine the correct conditions at the boundary. This is the chief result of our paper.” ↩
104.
Guth, Alan H. “Inflation.” Carnegie Observatories Astrophysics Series, Measuring and Modeling the Universe 2. 2004. A review of inflation by Alan Guth of MIT, written for a multi-author volume edited by W. L. Freedman, that explains how inflation works and how it shapes the pattern in the cosmic microwave background. It argues that inflation which is eternal into the future cannot be complete into the past, so some other physics would be needed to describe the beginning. The article uses it for Guth's own caution that eternal inflation does not establish a unique beginning. Mirror: arXiv
1. 104a.
  Section §1.7 Does Inflation Need a Beginning?, page 19: “There is of course no conclusion that an eternally inflating model must have a unique beginning, and no conclusion that there is an upper bound on the length of all backwards-going geodesics from a given point… The theorem does show, however, that an eternally inflating model of the type usually assumed… cannot be complete. Some new physics (i.e., not inflation) would be needed to describe the past boundary of the inflating region.” ↩
105.
Vilenkin, Alexander. “The Beginning of the Universe.” Inference: International Review of Science 1(4). 2015. An essay by Alexander Vilenkin in the magazine Inference, which the magazine labels a critical essay. It reviews the Penrose singularity theorem, eternal inflation and the Borde-Guth-Vilenkin (BGV) theorem on whether the universe had a beginning. Vilenkin is one of the three authors of the BGV theorem, and the article uses him because he says the universe probably had a beginning while also saying the theorem tells us nothing about God.
1. 105a.
  “The answer to the question, 'Did the universe have a beginning?' is, 'It probably did.' We have no viable models of an eternal universe. The BGV theorem gives us reason to believe that such models simply cannot be constructed.” He also stresses the theorem's generality: “It makes no assumptions about gravity or matter.” ↩
2. 105b.
  “Both sides have appealed to the BGV theorem, both sides appealing to me—of all people!—for a better understanding. … But my own view is that the theorem does not tell us anything about the existence of God.” He also writes: “Modern physics can describe the emergence of the universe as a physical process that does not require a cause,”. and concedes that. “The theory of quantum creation is no more than a speculative hypothesis. It is unclear how, or whether, it can be tested observationally.” ↩
106.
Ellis, George F. R., and Roy Maartens. “The Emergent Universe: Inflationary cosmology with no singularity.” Classical and Quantum Gravity 21:223. 2004. A paper proposing a closed universe that starts as a small static Einstein universe, inflates, and then reheats into the hot Big Bang, so that it has no singularity at the beginning. The article lists it among Big Bang models that keep the hot early phase but have no singularity. Mirror: arXiv
1. 106a.
  “These cosmologies have no singularity, no 'beginning of time', and no horizon problem.” Vilenkin's objection is that a static universe is unstable with respect to quantum collapse. ↩
107.
Planck Collaboration; SPT-3G; SH0ES; community analysis. Measurements of the Hubble constant H₀. n.d. Planck 2018 VI gives H₀ = 67.4 ± 0.5. SPT-3G D1 alone gives 66.66 ± 0.60 (arXiv:2506.20707). SH0ES gives 73.2 ± 0.9 (arXiv:2408.11770). The 117-author community analysis gives 73.50 ± 0.81 (A&A 708:A166, 2026, arXiv:2510.23823), and it does not include Freedman, Madore, Jang, Hoyt or Lee. Significances range from 4.5σ (DESI BAO+BBN against SH0ES, independent of the CMB) to 7.1σ. Both ends of the range give an age near 13 billion years: H₀ = 73.5 with Ω_m = 0.30 gives 12.8 Gyr, and H₀ = 68.5 gives 13.8 Gyr. A set of published measurements of the present rate of expansion, from the Planck 2018 analysis, the South Pole Telescope's 2025 data, the SH0ES distance-ladder work, and a 117-author community analysis from 2026. The article sets the microwave figures against the distance-ladder figures to show that the two routes disagree. ↩
108.
Efstathiou, George. “Challenges to the ΛCDM cosmology.” Philosophical Transactions of the Royal Society A 383:20240022. 2025. A paper on the challenges to ΛCDM, the standard cosmological model, published in the Philosophical Transactions of the Royal Society A. The article uses it for the point that any new physics offered for the Hubble tension must still reproduce the microwave background almost exactly. Mirror: arXiv
1. 108a.
  Section §2: “If it is argued that new physics beyond ΛCDM is required to explain, for example, distance scale measurements of the Hubble constant (the 'Hubble tension'), galaxy weak lensing measurements, (the 'S8 tension'), evolving dark energy, or bulk flow anomalies … then that new physics must reproduce the CMB anisotropies of the base ΛCDM cosmology to extraordinarily high precision.” ↩
109.
Freedman, Wendy L. et al. “Status Report on the Chicago-Carnegie Hubble Program (CCHP).” Astrophysical Journal 985:203. 2025. A status report from the Chicago-Carnegie Hubble Program, which measures the Hubble constant (the rate at which the universe expands) with the James Webb Space Telescope and red giant stars, using supernovae as calibrators. Its best value from the red-giant-branch method with 24 supernova calibrators is H₀ = 70.39. The erratum is at doi:10.3847/1538-4357/ae146d. The article uses it for the program's withdrawn Cepheid number.
1. 109a.
  Section 4: “In the case of the Cepheid distance scale, subsequent tests after unblinding revealed an issue in the data pipeline and in the photometric reductions of the HST data. A re-analysis of these data is on-going.” The passage is about the withdrawal of the v1 Cepheid number. Their published values: TRGB with 24 SN calibrators, H₀ = 70.39; JWST-only TRGB, 68.81; JWST-only JAGB, 67.80. ↩
110.
Planck Collaboration. “Planck 2018 results. VII. Isotropy and statistics of the CMB.” Astronomy & Astrophysics 641:A7. 2020. A Planck team paper on whether the microwave background looks the same in every direction and follows the statistics the standard model predicts. It is not Planck 2018 IX, which covers primordial non-Gaussianity. The article quotes its verdict that the evidence for a violation of isotropy remains unclear. Mirror: arXiv
1. 110a.
  Section 6: “The existence of these features is uncontested, but, given the modest significances at which they deviate from the standard ΛCDM cosmological model, and the a posteriori nature of their detection, the extent to which they provide evidence for a violation of isotropy in the CMB remains unclear. It is plausible that they are indeed simply statistical fluctuations.” For the current significances after the 2026 low-mask reanalysis, see Herold et al., ApJ 1005:146. ↩
111.
Bennett, C. L. et al. “Are There Cosmic Microwave Background Anomalies?” ApJS 192:17. 2011. A 2011 paper in the Astrophysical Journal Supplement Series, on claimed anomalies in the microwave sky. The article uses it for the authors' warning against after-the-fact statistics, which they illustrate with a coincidence in their own temperature map.
1. 111a.
  Section §7: “one of the authors (L.P.) noted that the initials of Stephen Hawking appear in the temperature map… We pose the question, what is the probability of this occurrence? It is certainly infinitesimal; in fact, much less likely than several claimed cosmological anomalies. Yet, we do not take this anomaly seriously because it is silly.” ↩
112.
Labbé, Ivo et al. “A population of red candidate massive galaxies ~600 Myr after the Big Bang.” Nature 616:266–269. 2023. A 2023 paper by a team of astronomers who used the first JWST images from the CEERS survey to look for massive galaxies about 600 million years after the Big Bang. It reports six candidates and says their masses and redshifts are not definitive. The article uses it as the case of the 2022 headlines about galaxies too massive to exist, which did not survive spectroscopy.
1. 112a.
  The v1 preprint (25 July 2022) was titled "A very early onset of massive galaxy formation" and claimed. “seven galaxies with M>10¹⁰ M_sun and 7<z<11 … including two galaxies with M~10¹¹,”. plus a forecast of galaxies out to z~18. The published version claims six candidates over 7.4<z<9.1, with one "possible" 10¹¹, and the z~18 forecast deleted. The in-paper hedges say. “these masses and redshifts are not definitive and that all galaxies should be considered candidates,”. “All objects in this paper should be considered candidate massive galaxies, to be confirmed with spectroscopy.” Later spectroscopy: every spectroscopic redshift came in lower than the photometric estimate, and L23-13050 turned out to be a broad-line AGN (a black hole feeding on gas, which outshines its galaxy) at z = 5.624. ↩
113.
Macquart, J.-P. et al. “A census of baryons in the Universe from localized fast radio bursts.” Nature 581:391–395. 2020. A paper in Nature that weighs the ordinary matter (baryons) in the universe. It uses localized fast radio bursts, brief bright radio flashes from distant sources, and measures the dispersion of their signals, which tells how much gas they pass through. The article uses it to answer where the missing baryons went.
1. 113a.
  The dispersion measures of localised fast radio bursts weigh the entire intergalactic medium, recovering the full baryon content predicted by nucleosynthesis and the CMB. With Nicastro et al., Nature 558 (2018): 406, this closes the missing baryons problem raised in López-Corredoira's §4.1. ↩
114.
Lerner, Eric J. et al. “An Open Letter to the Scientific Community.” New Scientist. May 22, 2004. A public letter in New Scientist that urges funding for alternatives to the big bang. It was signed by thirty-four original signatories, including Hermann Bondi and Thomas Gold, two of the three authors of the steady-state theory, and Jayant Narlikar, Hoyle's student and co-author. The article quotes its complaint that the big bang relies on entities nobody has observed.
1. 114a.
  “The big bang today relies on a growing number of hypothetical entities, things that we have never observed — inflation, dark matter and dark energy are the most prominent examples. Without them, there would be a fatal contradiction between the observations made by astronomers and the predictions of the big bang theory. In no other field of physics would this continual recourse to new hypothetical objects be accepted as a way of bridging the gap between theory and observation.” Carl Wieland's response for Creation Ministries International miscounts the signatories as 33. ↩
115.
Carroll, Sean. “Doubt and dissent are not tolerated.” Preposterous Universe. May 29, 2004. A blog post by Sean Carroll answering an online petition against the Big Bang model, which the post says was first published in New Scientist. The article uses it for Carroll's list of confirmed predictions and for his reply to the petition's claim that doubt is not tolerated.
1. 115a.
  The words answer the petition's claim that the Big Bang has no quantitative predictions that were later confirmed by observation. “Really? How about acoustic peaks in the power spectrum of temperature fluctuations in the cosmic microwave background? And the polarization signal, and its spectrum? And the baryon density as deduced from light-element abundances agreeing with that deduced from the CMB? And baryon fluctuations in the power spectrum of large-scale structure? And the transition from acceleration to deceleration in the Hubble diagram of high-redshift supernovae? And the relativistic time delay in supernova light curves?” ↩
2. 115b.
  Carroll is answering Eric Lerner, a petition signatory and author of The Big Bang Never Happened, who wrote that the dark energy field violates conservation of energy. “Actually, there is a field of physics in which energy is not conserved: it's called general relativity. In an expanding universe, as we have known for many decades, the total energy is not conserved… Every photon loses energy by redshifting as the universe expands, while the total number of photons remains conserved, so the total energy decreases. An effect which has, of course, been observed.” ↩
3. 115c.
  The post answers the petition's claim that doubters fear losing their funding. “And yes, young people who disbelieve in the Big Bang are unlikely to get invited to speak at major conferences, or get permanent jobs at research universities. Likewise astrophysicists who believe in astrology, or medical doctors who use leeches to fight cancer.” ↩
4. 115d.
  “And to be sure, the alternatives to the Big Bang are just silly… They just aren't, for the most part, very smart.” ↩
116.
Lerner, Eric J. “Observations contradict galaxy size and surface brightness predictions that are based on the expanding universe hypothesis.” Monthly Notices of the Royal Astronomical Society 477(3):3185–3196. 2018. A single-author paper by a working experimental plasma physicist with refereed papers in Physics of Plasmas, arguing that galaxy sizes contradict the expanding universe. The article gives it as the one honest note on Lerner: a real paper in a refereed journal that has not been answered in print.
1. 116a.
  Abstract: “We show that the radii data for both disc and elliptical galaxies are incompatible with any of the published size-evolution predictions based on an expanding universe.” Twenty-seven citations as of August 2026, mostly in alternative-cosmology venues, and no published rebuttal. Lerner's widely circulated JWST claim appeared in IAI News (11 August 2022), a magazine, not a journal. ↩
117.
Ćirković, Milan M. “Laudatores Temporis Acti, or Why Cosmology is Alive and Well — A Reply to Disney.” General Relativity and Gravitation 34:119–130. 2002. An essay replying to a 2000 critique of cosmology by Disney, which said that cosmology's claims are overblown. The author argues that modern cosmology rests on sounder empirical and philosophical foundations than that critique allows, and that similar complaints have a long history. The article uses it for the author's point that the one-universe objection would also cast doubt on biology, history, geology and archaeology.
1. 117a.
  “In several instances, Disney suggests that the status of cosmology as a science is somehow jeopardized by the fact that there is only a single universe. Per analogiam, it is highly uncertain whether evolutionary biology is a science (there has been only one, unrepeatable evolution of terrestrial biosphere), whether history is a science (unrepeatable sequence of historical events), whether geology is a science (only one Earth!), whether archaeology is a science (only a single array of material traces of ancient cultures), etc.” ↩
118.
Hartnett, John G. “Big bang casts no shadows and the retraction.” Journal of Creation 32(2):3–4. 2018. A 2018 retraction in the creationist Journal of Creation of Hartnett's earlier argument that the expected shadows of galaxy clusters are missing from the microwave background, and that this counted against the Big Bang. The article uses it as the clearest case of a creationist withdrawing an argument in print.
1. 118a.
  “Without anything to contradict this new result, and the analysis seems strong, one must entertain the possibility that the anomaly first found by Lieu et al in 2006 has been adequately explained… At best this no-shadow argument is now equivocal and hence I suggest that it should no longer be used as an argument against the big bang hypothesis.” The paper that changed his mind is Xiao, Chen, Zhang, Wu & Dai, MNRAS Letters 432 (2013): L41. ↩
119.
Hartnett, John G. “Quantized quasar redshifts in a creationist cosmology.” Astrophysics and Space Science 324:13. 2009. A 2009 paper by the creationist John Hartnett arguing that quasar redshifts come in fixed steps. The article uses it because periodicity in quasar counts was the strongest form of that claim, and Hartnett's own check of the survey's reliability flag undercut it. Mirror: arXiv
1. 119a.
  The same periods appear in the survey's own zConf reliability flag, so Hartnett wrote: “these redshift periods must result from some selection effect… It does not signal any intrinsic (quantized) redshifts in the quasars.” Bell and Comeau, in Astrophysics and Space Science 326:11 (2010), identified the mechanism: emission lines crossing SDSS filter gaps imprint. “a periodicity of Delta(z)~0.6.” ↩
120.
Thomas, Brian. “Big Bang Fizzles under Lithium Test.” Creation Science Update (Institute for Creation Research). Sep 22, 2014. A short online article by Brian Thomas, Ph.D., on the website of the Institute for Creation Research, about a laboratory test of the lithium prediction of Big Bang nucleosynthesis. The test ran at the LUNA accelerator in Italy, and the piece reports that it matched the predicted lithium ratio. The article uses it to show that the piece cites an experiment that closed the lithium-6 problem and then claims that the universe has too much lithium-6.
1. 120a.
  “Unfortunately for Big Bang theorists, their experiment succeeded. The details, published in Physical Review Letters, demonstrated that if lithium actually formed by some primordial nucleosynthesis, it should indeed have formed in the predicted ratio. And that's a big problem for the Big Bang.” Two paragraphs later the piece says: “Put simply, the universe has way too much lithium-6 than the Big Bang could produce.” The experiment cited (Anders et al., PRL 113:042501, 2014, at LUNA) measured the ²H(α,γ)⁶Li cross-section and removed the claimed lithium-6 anomaly. The lithium-6 "second lithium problem" was independently closed by Lind, Meléndez, Asplund et al., A&A 554 (2013): A96, who showed the claimed detections were an artifact of neglected line asymmetries. Lithium-7 remains a real problem. ↩
121.
Super-Kamiokande Collaboration. Search for proton decay via p → e+π0. n.d. A search for one way a proton could decay, into a positron and a neutral pion, which found no candidate events and a partial-lifetime limit above 10^34 years. Every grand unified theory predicts proton decay, and none has been confirmed. The article uses it to show that the magnetic-monopole problem that inflation is credited with solving rests on an unverified premise. ↩
122.
Clark, S. E. et al. “Neutral Hydrogen Structures Trace Dust Polarization Angle: Implications for Cosmic Microwave Background Foregrounds.” Physical Review Letters 115:241302. 2015. A study of how structures in neutral hydrogen gas (HI) in our galaxy line up with the angle of polarized dust emission, and what that means for the foreground signal that must be removed from CMB maps. The article uses it to show which part of Verschuur's claim holds up.
1. 122a.
  Establishes that Galactic HI filaments trace the orientation of Planck's 353 GHz polarized dust emission — the part of Verschuur's claim that is real, now used to build B-mode foreground templates. It does not establish any correlation with the primary CMB anisotropies. ↩
123.
Luminet, Jean-Pierre. “Editorial note to: Georges Lemaître, The beginning of the world from the point of view of quantum theory.” General Relativity and Gravitation 43. 2013. An editorial note on Georges Lemaître's paper "The beginning of the world from the point of view of quantum theory." It quotes Lemaître's letter of 9 March 1931 to W. M. Smart, which shows that Lemaître himself made the cut in the English translation of his 1927 paper. The article uses it for the Lemaître Archives report of a sentence about God that Lemaître deleted.
1. 123a.
  Luminet reports from the Lemaître Archives that Lemaître deleted a sentence about God from the Nature manuscript before publication. Its point being that God is hidden and physics is a veil over creation. ↩
124.
Hoyle, Fred. The Nature of the Universe. Mentor (New York). 1950 (edition of 1955). A book of Hoyle's BBC radio talks on the universe, the broadcasts in which he coined the phrase "big bang." The original edition was published by Blackwell in Oxford in 1950. The article uses it for Hoyle's own objections to the big bang, in his words.
1. 124a.
  Page 113: “On scientific grounds this big bang assumption is much the less palatable of the two. For it is an irrational process that cannot be described in scientific terms… On philosophical grounds too I cannot see any good reason for preferring the big bang idea. Indeed it seems to me in the philosophical sense to be a distinctly unsatisfactory notion, since it puts the basic assumption out of sight where it can never be challenged by a direct appeal to observation.” Page 109: “This big bang idea seemed to me to be unsatisfactory even before detailed examination showed that it leads to serious difficulties.” ↩
125.
Eddington, A. S. “The End of the World: from the Standpoint of Mathematical Physics.” Nature 127(3203):447–453. Mar 21, 1931. An article in Nature by A. S. Eddington, written from the standpoint of mathematical physics. The article uses it for Eddington's concession that the evidence points to a boundary, a beginning of time, that cannot be climbed over.
1. 125a.
  Page 450: Given in full. “I have no 'philosophical axe to grind' in this discussion. Philosophically, the notion of a beginning of the present order of Nature is repugnant to me. I am simply stating the dilemma to which our present fundamental conception of physical law leads us. I see no way round it; but whether future developments of science will find an escape I cannot predict.” Lemaître quotes the sentence back at Eddington in Nature 127 (1931): 706, which independently confirms the wording and the qualifier. ↩
2. 125b.
  Page 450: “we find the sweepings all piled up like a high wall and forming a boundary—a beginning of time—which we cannot climb over.” ↩
126.
Lisle, Jason. Taking Back Astronomy. Master Books. 2006. Page 33. A 2006 book by Jason Lisle, cited here for the star count he gives in it. The article uses it to show what young-earth cosmology accepts about the size of the universe.
1. 126a.
  In Lisle's words, stars number. “10²², or ten billion trillion, give or take a factor of ten or so.” No young-earth cosmology reduces the star count; they dispute distance, age and geometry, not the census. ↩
127.
Faulkner, Danny R. “How Big Is the Universe?” The New Answers Book 4, chapter 18; republished by Answers in Genesis. Jan 25, 2020. A chapter by the young-earth astronomer Danny Faulkner, in a creationist book, on how astronomers measure distances from nearby stars out to distant galaxies. It concludes that every method gives distances of millions or billions of light-years, and that its errors would not shrink them to thousands. The article uses it because the creationist author accepts that the distances are as large as astronomers say.
1. 127a.
  Section Conclusion: How Big is the Universe: “those errors would not reduce the distances down to just thousands of light-years”. “Many recent creationists worry about the light travel time problem and entertain possibilities of the universe being far smaller than generally thought as a way out of this dilemma. But thinking this stumbles over something that ought to be obvious.” ↩
128.
Faulkner, Danny R. “Problems with the Big Bang.” Universe by Design. Master Books. 2004 (edition of 2013). Chapter 4 of a creationist book by Dr. Danny R. Faulkner, which argues against the Big Bang on quasars, Halton Arp's redshift claims, quantized redshifts, the COBE results and the cosmological principle. Answers in Genesis republished it online on 11 June 2013 as current content. The article uses it because the publisher still hosts it, although Faulkner's own 2018 paper contradicts it.
1. 128a.
  Section The CBR: “As the first data from COBE were assembled in the early 1990s, we found that the CBR was perfectly smooth.” This is false: COBE's DMR instrument detected the anisotropies, work that won the 2006 Nobel Prize in Physics. The same chapter endorses Halton Arp and treats redshift quantisation as a live problem, both positions Faulkner himself dismantles in his 2018 paper. AiG has not withdrawn or annotated it. ↩
129.
Ross, Hugh. “Big Bang—The Bible Taught It First!” Reasons to Believe. Jul 1, 2000. A popular article by Hugh Ross of Reasons to Believe, arguing that the Bible described the big bang's two main features before any scientist did. It counts eleven verses that describe the heavens as stretched out, and it reads the Hebrew verb forms as meaning that the stretching is both finished and ongoing. The article uses it as the apologetic claim that Scripture taught the big bang first, and it answers that claim.
1. 129a.
  Ross writes: “The Bible's prophets and apostles stated explicitly and repeatedly the two most fundamental properties of the big bang, a transcendent cosmic beginning a finite time period ago and a universe undergoing a general, continual expansion.” His eleven "stretched out" verses are Job 9:8; Psalm 104:2; Isaiah 40:22; 42:5; 44:24; 45:12; 48:13; 51:13; Jeremiah 10:12; 51:15; and Zechariah 12:1. Isaiah 40:22 completes its own simile, "and spreads them out like a tent to dwell in," which is standard ancient Near Eastern imagery for the sky rather than a description of metric expansion. ↩
130.
Wieland, Carl. “Secular scientists blast the big bang: What now for naïve apologetics?” Creation 27(2):23–25. Mar 2005. A magazine article by Carl Wieland of Creation Ministries International, written as a reply to a 2004 open letter in which 33 scientists criticized the Big Bang. It argues that the Big Bang's sequence of events and its billions of years are incompatible with the Bible. The article uses it for the most memorable statement of the creationist objection to accepting the Big Bang into Christian thought.
1. 130a.
  “We have long warned that adopting the big bang into Christian thought is like bringing the wooden horse within the walls of Troy,”. “Marrying one's theology to today's science means that one is likely to be widowed tomorrow.” ↩