Cosmic Inflation

Inflation answers a real puzzle, the horizon problem, and made one prediction that could have failed and did not: the slight tilt of the primordial spectrum, measured at 8 to 10 sigma. But its gravitational waves remain undetected, its flatness argument is disputed inside mainstream cosmology, and its own architects disagree in print over whether it can be falsified.

By AI (Claude Opus 5, thinking level unavailable); strengthening review by Claude Opus 5.5, thinking level unavailable Draft:  August 2026

Summary

  • Inflation is the proposal that space expanded by a factor of at least 1026 in a small fraction of the first second, driven by a field whose energy pushes outward instead of pulling inward. Alan Guth published it in 1981 to fix three problems in the standard hot big bang at once.
  • Only one of those three problems is in good shape. The horizon problem is real, and the cosmologists most hostile to the flatness argument say so in the same paper. The flatness problem is disputed inside mainstream cosmology in unusually blunt language — one MNRAS paper calls the standard version "completely bogus." The monopole problem depends on grand unified theories that have never been observed, and proton decay has not been seen past 1034 years.
  • Guth's own model did not work, and he said so in the paper that proposed it. Old inflation could start but could not stop cleanly. The fix — new inflation, then chaotic inflation — replaced the mechanism entirely within two years.
  • "Inflation" is now a family, not a theory. A 2013 Bayesian survey compared 193 single-field slow-roll models against Planck data. The library behind it has grown from 64 implemented models in 2013 to 118 in 2024, and a 2024 paper marginalises over "nearly 300."
  • Inflation made one genuine advance prediction that could have failed and did not: the slight tilt. Planck measures the spectral index at ns = 0.9649 ± 0.0042, eight standard deviations from a perfectly scale-invariant spectrum, and on the side the simplest models require. The 2025 combination of Planck with the Atacama Cosmology Telescope, the South Pole Telescope and BICEP/Keck tightens it to ns = 0.9682 ± 0.0032, about ten standard deviations from 1. The perturbations are also adiabatic and Gaussian to high precision, as predicted. This is a real success and any article that skips it is not honest.
  • But scale invariance itself was not inflation's idea. Harrison and Zel'dovich proposed it in 1970, eleven years earlier. Andrei Linde concedes the point in print. Only the sign and size of the departure from it belong to inflation.
  • The prediction inflation is most identified with has never been found. Primordial gravitational waves would show up as a curl pattern in microwave-background polarisation. The best limit from B-mode data is still r0.05 < 0.036, from BICEP/Keck's 2018 season, published in 2021. Adding Planck, the newer ground telescopes and galaxy surveys moves it only to r < 0.032 to 0.034, because no newer B-mode data have beaten it.
  • In 2014 a detection was announced and it was Galactic dust. BICEP2 reported r = 0.20, with r = 0 ruled out at 7.0σ. Within six months Planck showed the dust in that patch of sky was "comparable in magnitude" to the whole signal. The joint analysis found "no statistically significant evidence for tensor modes."
  • No finite upper limit on r can rule out inflation as a class, because one popular model family drives r arbitrarily close to zero by turning down one parameter. That is the asymmetry at the heart of the falsifiability dispute.
  • The sharpest critique is internal. Paul Steinhardt helped build inflationary theory and now argues it "cannot be evaluated using the scientific method." Thirty-three physicists including Guth, Linde, Stephen Hawking, Steven Weinberg and Edward Witten replied in print that "standard inflationary models could have failed any of the empirical tests described above, but they did not." Both sides are quoted at length below.
  • The measure problem is the real hinge, and both sides concede it is unsolved. Guth, David Kaiser and Yasunori Nomura wrote that "a persuasive theory of probabilities in the multiverse has not yet been found." Everything about probability in an eternally inflating universe rests on that gap.
  • For a Christian reader: inflation is neither an argument for creation nor against it. It is a mechanism inside a model of the deep past. Creationist writers who name it as the weak floor of big bang cosmology have picked the right layer, but the reasons usually given are imprecise, and two of the three commonly cited problems do not carry the weight put on them.

This is a case file under the standard model overview, which treats inflation in a few paragraphs.  The multiverse that eternal inflation produces has its own article and is covered here only as far as the falsifiability argument requires.

What inflation actually claims

Start with the mechanism, because the arguments make no sense without it.

In the standard hot big bang, gravity always slows the expansion down.  Matter and radiation both attract.  Run the film forward and the expansion rate falls.

Inflation says that for a brief window very early on, the universe was dominated by a different kind of energy — a scalar field, usually called the inflaton, sitting at high potential energy.  A field like that has negative pressure.  In general relativity, pressure gravitates, and sufficiently negative pressure makes gravity repulsive.  So the expansion accelerates instead of decelerating.

While that lasts, distances double at a fixed rate.  Double them sixty times and you get a factor of about 1026.  That is the standard requirement, and it is set by what the fix has to accomplish, not derived from anything deeper.

Then it has to stop.  The field rolls down its potential to the bottom, oscillates, and dumps its energy into ordinary particles.  That step is called reheating, and it is what makes the hot big bang hot.  In this picture the "bang" is not the beginning; it is the end of inflation.

Three consequences follow, and they are the whole of the case.

Everything we see today came from one tiny patch.  A region far smaller than a causally connected volume at that epoch was stretched to more than the size of the visible universe.  So the whole observable sky has a common history, which is why it has a common temperature.

Curvature is flattened.  Stretching any surface makes it locally flatter.  Sixty doublings makes any initial curvature undetectable.

Anything made before inflation is diluted to nothing.  If exotic relics like magnetic monopoles were produced earlier, the expansion drives their density to zero.

And one more, which was not part of the original design and turned out to matter most.  Quantum fluctuations in the inflaton field get stretched along with everything else.  A fluctuation that starts smaller than an atom ends up larger than a galaxy.  Those become the density ripples that seed galaxies, and they are what the microwave background measures.  This was worked out between 1981 and 1983, after Guth's paper, and it is the part of inflation that produced testable numbers.  It is treated in its own section below.

The three problems inflation was invented to solve

Guth's title names two of them:  "The Inflationary Universe:  A Possible Solution to the Horizon and Flatness Problems."1  The monopole problem is in section IV of the same paper.  They are not equally strong, and the differences matter more than the similarity.

The horizon problem is real

The microwave background is the same temperature everywhere to about one part in 100,000.  That is the puzzle.

Light travels at a finite speed, and the universe has a finite age.  So there is a maximum distance any signal could have travelled by any given moment.  Two patches of sky farther apart than that have never been able to exchange anything — no light, no heat, no particle.  Yet they match.

Guth put the count in his own paper.  For an initial temperature of 1017 GeV, the early universe "consists of at least ~1083 separate regions which are causally disconnected (i.e., these regions have not yet had time to communicate with each other via light signals).  Thus, one must assume that the forces which created these initial conditions were capable of violating causality."1  He then makes the point that the number is not an artefact of that choice.  Take a modest starting temperature of 1 MeV instead and you still get "at least ~1022 causally disconnected regions."1  The figure usually quoted for the patches on the sky today is of order 104, which is the same problem measured at the surface of last scattering rather than at the start.  Treat that as an order of magnitude:  the count changes depending on whether the particle horizon or the sound horizon is used.

The strongest thing that can be said for this problem is that the cosmologists who dismantle the flatness argument defend this one in the same paper.  Sean Carroll and Heywood Tam computed the natural measure on the space of solutions to Einstein's equations, and concluded:

The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat.  The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real.2

That is a hostile witness, and it is worth more than a friendly one.

Two honest qualifications belong with it.

First, nothing in general relativity forbids a smooth initial condition.  The horizon problem is not a case of the model contradicting itself.  It is a case of the model requiring an initial correlation it does not explain.  That is a real defect, but it is a different kind of defect from a quantity that exceeds a bound.

Second, inflation does not remove the problem so much as relocate it.  Carroll and Tam again, from the same paper:  "Inflation by itself cannot solve the horizon problem, in the sense of making the smooth early universe a natural outcome of a wide variety of initial conditions."2  Their reason is Liouville's theorem:  if evolution is reversible, no dynamical process can funnel many initial states into few final ones.  They still think inflation is worth having — it "provides an appealing target for true theories of initial conditions" — but that is a much weaker claim than the one usually made for it.2

The flatness problem is weaker than it is usually presented

The standard argument runs like this.  The density parameter Ω measures the average density against the value that makes space flat.  Ω = 1 exactly is an unstable equilibrium:  push it slightly above or below and it runs away fast.  Since Ω is near 1 today, it must have been fantastically close to 1 early on.

Guth's own numbers:  starting at 1017 GeV, "the value of H0 must be fine tuned to an accuracy of one part in 1055," and at 1 MeV, "one part in 1015."1  The 1060 figure quoted in popular accounts comes from running the same calculation back to the Planck time.

Three mainstream cosmologists say this argument is wrong, and none of them is a creationist.

Phillip Helbig, in Monthly Notices of the Royal Astronomical Society in 2012, describes the standard version as "completely bogus."3  His objection is that the argument treats Ω as though it were a parameter drawn at random, and then measures fine-tuning against a distribution nobody has justified.

Carroll and Tam reach the same conclusion by a different route.  Using the canonical measure on cosmological solutions, "we find that the flatness problem is an illusion; in the context of purely Robertson-Walker cosmologies, the measure diverges on flat universes."2  In plain terms:  if you count solutions to Einstein's equations in the only natural way anyone has found, nearly all of them are flat.  A flat universe is the generic case, not the special one.

Geraint Lewis and Luke Barnes concede it in A Fortunate Universe, a book arguing for fine-tuning:  on the Hawking-Page measure, flat universes have measure 100%, and "flat universes are utterly unsurprising."4

The Berean Archive's own fine-tuning article declines to use the flatness problem as evidence for anything, for exactly these reasons.  This article takes the same line.  It follows that one of inflation's three founding motivations was answering a question that may not have needed an answer.

That cuts in an awkward direction, and it is worth saying out loud.  If the flatness problem is an illusion, then flatness is not a success for inflation either — a theory does not get credit for explaining a non-problem.  What inflation does get credit for is the quantitative density prediction, which is a separate matter and is handled below.

The monopole problem rests on physics that has never been observed

Grand unified theories predict magnetic monopoles.  Guth's section IV works through the production rate and concludes that "far too many monopoles would be produced" in a standard cosmology with a grand unified phase transition.1  Inflation dilutes them away.

The difficulty is the premise.  No grand unified theory has ever been confirmed.  Its most accessible signature is proton decay, and proton decay has not been seen.  Super-Kamiokande's limit on the p → e+π0 channel is a partial lifetime above 2.4 × 1034 years.5  Every simple grand unified model that predicted decay faster than that is dead.

So the monopole problem is a problem in a theory that is itself unverified.  A defect in a hypothetical extension is not a defect in the standard hot big bang.  This article does not count it.

It is worth noticing that Guth himself framed it as a secondary motivation.  The title of his paper names the horizon and flatness problems; monopoles appear in section IV.  The popular retelling that lists three problems as equals is not how the founding paper presented them.

From one model to a family: 1980 to now

The word "inflation" today does not name Guth's theory.  It names a class of theories that share a shape.  The history explains why that matters, and it is a history in which the founding model failed within two years.

Guth's model could start but could not stop

Guth's mechanism was a first-order phase transition.  The universe cools below the temperature at which a symmetry should break, but gets stuck in the old, symmetric state — supercooled, like water below freezing that has not yet turned to ice.  That stuck state has energy, and that energy drives exponential expansion.  Eventually bubbles of the true, lower-energy state nucleate at random, grow, and fill space.  The transition finishes and the released latent heat becomes the hot big bang.

That last step does not work, and Guth said so in the paper.  His section V is titled "Problems of the Inflationary Scenario," and opens by stating that the scenario "seems to lead to some unacceptable consequences."1  The specific failure:

The central problem is the difficulty in finding a smooth ending to the period of exponential expansion… The randomness of the bubble formation process then leads to gross inhomogeneities.1

The trap is a squeeze.  Bubbles have to nucleate slowly, or inflation stops too soon to accomplish anything.  But if they nucleate slowly, the space between them keeps inflating faster than the bubbles can grow, and they never merge into a smooth universe.  Guth and Erick Weinberg proved the general case in 1983 in a paper whose title asks the question directly:  "Could the Universe Have Recovered from a Slow First Order Phase Transition?"6  The answer was no.  This is called the graceful exit problem.

Linde's summary of it, thirty years later, is compact:

If the probability of the bubble formation is large, bubbles of the new phase are formed near each other, inflation is too short to solve any problems, and the bubble wall collisions make the universe extremely inhomogeneous.  If they are formed far away from each other, which is the case if the probability of their formation is small and inflation is long, each of these bubbles represents a separate open universe with a vanishingly small Ω.  Both options are unacceptable.7

Guth's closing sentence is the one to remember, because nothing written about inflation since has been this modest:

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.1

New inflation replaced the mechanism

The fix came from Andrei Linde in 1982 and, independently and three months later, from Andreas Albrecht and Paul Steinhardt.89  Instead of a field trapped in a false vacuum waiting for bubbles, the field starts near the top of a very flat potential and rolls slowly down.  Inflation happens during the roll, not during the wait.  One region inflates into something larger than the observable universe, so there are no bubble walls inside our sky to make it lumpy.

That solved the exit.  It created new problems.  Linde lists them in his own review:  the inflaton "must have an extremely small coupling constant, so it could not be in thermal equilibrium with other matter fields," which is what the whole phase-transition picture had assumed; and new inflation "could explain why our universe was so large only if it was very large and contained many particles from the very beginning."7

That second problem is the circularity charge, stated by a founder in 2014, thirty years before the critics made it famous.

Chaotic inflation threw out the phase transition entirely

Linde's 1983 paper abandoned the framework.10  No thermal equilibrium, no phase transition, no grand unified theory.  Just a scalar field with a simple potential — the textbook example is V(φ) = ½m²φ² — which happens to start at a large value somewhere.  Wherever it does, that patch inflates.  Chaotic inflation is what nearly all modern model-building descends from.

Linde is blunt about how much of the literature has not caught up:

This idea was abandoned by all experts actively working in this area of physics, but unfortunately it is still present in virtually all textbooks on astrophysics, which incorrectly describe inflation as an exponential expansion in a supercooled false vacuum state during the cosmological phase transitions in grand unified theories.7

This is worth pausing on.  The version of inflation most educated readers have been taught — Guth's supercooled false vacuum — is, on the account of one of inflation's own architects, not what anyone in the field has believed since 1983.  Popular criticism of inflation frequently attacks that dead version.  So does popular defence of it.

The model count

By the 2010s "inflation" covered enough distinct proposals that people started counting them.

Jérôme Martin, Christophe Ringeval and Vincent Vennin built a software library called ASPIC to compute predictions model by model.  The first Encyclopædia Inflationaris in 2013 covered 64 implemented models.11  The 2024 revision covers 118, and describes "the size of the inflationary landscape which contains hundreds of different scenarios."11  A 2024 companion paper marginalises over "nearly 300 models of single-field slow-roll inflation."12

And these are only the simplest kind — single field, minimal kinetic term, slow roll.  Multi-field models, non-minimal couplings and everything else are outside the count.

The most useful thing anyone has done with that list is the 2013 Bayesian comparison by Martin, Ringeval, Roberto Trotta and Vennin.  They ran 193 models against Planck 2013 data and reported:

Our analysis singles out the most probable models (from an Occam's razor point of view) that are compatible with Planck data, while ruling out with very strong evidence 34% of the models considered.  We identify 26% of the models that are favoured by the Bayesian evidence, corresponding to 15 different potential shapes.  If the Bayesian complexity is included in the analysis, only 9% of the models are preferred, corresponding to only 9 different potential shapes.  These shapes are all of the plateau type.13

Read that carefully, because it cuts both ways.  Planck data killed a third of the models outright, which is a real empirical result and not what an untestable theory looks like.  But two-thirds survived, and after the best data ever taken there were still nine distinct potential shapes standing.

That is the situation the falsifiability argument is about.

What inflation predicted before it was measured

This is the part a critic of inflation is most tempted to skip, and skipping it is how an article loses a technically literate reader in one paragraph.  Inflation made specific quantitative predictions.  They were made before the measurements.  They came out right.

The clearest statement of the list is by the thirty-three physicists who replied to Steinhardt in 2017:

The standard inflationary models predict that the universe should have a critical mass density (that is, it should be geometrically flat), and they also predict the statistical properties of the faint ripples that we detect in the cosmic microwave background (CMB).  First, the ripples should be nearly "scale-invariant," meaning that they have nearly the same intensity at all angular scales.  Second, the ripples should be "adiabatic," meaning that the perturbations are the same in all components:  the ordinary matter, radiation and dark matter all fluctuate together.  Third, they should be "Gaussian," which is a statement about the statistical patterns of relatively bright and dark regions.  Fourth and finally, the models also make predictions for the patterns of polarization in the CMB, which can be divided into two classes, called E-modes and B-modes.14

Take them one at a time.

The density prediction

Inflation drives Ω to 1.  Guth published that in 1981.  The decisive measurement was BOOMERanG's balloon flight over Antarctica, reported in Nature on 27 April 2000:  "Marginalizing over all the other parameters, we found the following 95% confidence interval for Ω0 = Ωm + ΩΛ:  0.88 < Ω0 < 1.12.  This provides evidence for a euclidean geometry of the Universe."15  Nineteen years after the prediction.  Planck plus baryon acoustic oscillation data now has it flat to 0.4%.16

The 2017 letter puts the weight on how uncertain the number was at the time:

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.)14

That is a fair point and it should be granted.  But it needs a hard qualification, and the qualification comes from inflation's own architects.

Linde, writing 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.7

Those models are real, published in Physical Review D, and citable:  "An open universe from inflation" by Martin Bucher, Alfred Goldhaber and Neil Turok, and "Inflation with Ω ≠ 1" by Linde and Arthur Mezhlumian, both in 1995.1718

Viatcheslav Mukhanov is blunter:  the flatness prediction "was first confirmed only at the end of 90th with the discovery of dark energy.  Note that the experimental data before were in strong disagreement with it."19

So the honest scoring is this.  Inflation predicted Ω = 1 in 1981.  The data through the 1990s pointed elsewhere.  Inflationists built models for the other answer.  Then the data came back to Ω = 1 and the prediction was declared confirmed.  A theory whose defenders have a version ready for whichever way the data goes cannot bank the full value of a hit.  It is still a hit.  It is not the clean hit the retelling makes it.

The tilt — this one is a real success

This is the strongest item in inflation's favour and it deserves its number.

Scale invariance means fluctuations have the same strength at every size.  Perfect scale invariance is ns = 1.  Inflation cannot deliver exactly 1:  the field is rolling, so conditions change slightly as different scales leave the horizon, and the spectrum comes out slightly tilted.  For the simplest models the tilt is red — slightly more power on large scales — and of order a few percent.

Planck measures ns = 0.9649 ± 0.0042.16  That is eight standard deviations away from 1.20  It is on the predicted side and of the predicted size.

The newer telescopes have made the number firmer, not weaker.  Combining Planck with the Atacama Cosmology Telescope's 2025 data release, the South Pole Telescope and BICEP/Keck gives ns = 0.9682 ± 0.0032, about ten standard deviations from 1.2122

Linde is entitled to the victory lap he takes:  "Now the Harrison-Zeldovich spectrum is ruled out at the 5σ level, and inflationary expectations are confirmed."7

But note what he is comparing against, because it is the necessary caveat.  Scale invariance was not inflation's idea.  Edward Harrison proposed it in Physical Review D in 1970 and Yakov Zel'dovich in MNRAS in 1972, eleven and nine years before Guth.2324  Linde concedes it in the same paragraph:  "critics of inflation argued that the prediction ns = 1 is trivial because it was made by Harrison and Zeldovich (albeit without any real physical motivation) long before inflation."7

So the credit due to inflation is precise:  not scale invariance, but the small departure from it, and the sign of that departure.  That is a smaller claim than "inflation predicted the CMB fluctuations."  It is also a real one, and this article does not discount it.

Adiabatic and Gaussian

Adiabatic means all components — photons, baryons, dark matter, neutrinos — fluctuate together, as they would if a single field's fluctuations set the density everywhere.  The competing possibility, isocurvature, means the components vary against each other.  Planck constrains the non-adiabatic contribution to the observed temperature variance to 1.3% for cold dark matter and 1.7% for the neutrino modes, at 95% confidence.16

Gaussian means the fluctuations are drawn from a normal distribution with no preferred skew, which is what free quantum fields produce.  The standard measure is fNL.  Planck's combined temperature-and-polarisation result is fNLlocal = −0.9 ± 5.1.25  Consistent with zero, which is what the simplest single-field models predict.

Planck's own summary sentence:  "All these findings support the key predictions of the standard single-field inflationary models."16

There is a citation trap here worth flagging, because the 2017 open letter falls into it.  The letter quotes "the Planck results offer powerful evidence in favour of simple inflationary models" and attributes it to "the Planck satellite team" in 2016.14  The sentence is in Planck 2015 results XIII, the cosmological-parameters paper, not in XX, the inflation paper.  Anyone chasing the reference to the obvious place will not find it.

Correlations larger than the horizon

The subtlest confirmation is a phase relationship.  If density ripples were already in place before a region could have made them causally, the temperature and polarisation of the microwave background should be anticorrelated at large angles in a specific way.  WMAP found it.

The discovery paper's own hedge has to travel with the result:

In addition to inflation, the pre-Big-Bang scenario and the Ekpyrotic scenario predict the existence of superhorizon fluctuations.26

So it confirms some epoch that put fluctuations outside the horizon.  It does not pick inflation out of the field.  Steinhardt's own bouncing models pass this test.

What has not been found: primordial gravitational waves

Inflation stretches quantum fluctuations in the gravitational field the same way it stretches fluctuations in the inflaton.  Those become gravitational waves — ripples in spacetime with wavelengths the size of the visible universe.  Nothing else in cosmology makes them, which is why they are called the smoking gun.

They would leave a distinctive curl pattern, called B-mode polarisation, in the microwave background.  Their strength is measured by the tensor-to-scalar ratio r.

They have not been found.

The limits, with their dates

The BICEP/Keck collaboration gives its own history in one sentence:

The BKP analysis yielded a 95% confidence constraint r0.05 < 0.12, which BK14 improved to r0.05 < 0.09, and BK15 improved to r0.05 < 0.07.  The BK18 result described in this letter, r0.05 < 0.036, represents a fractional improvement equivalent to the two previous steps combined.27

That 2021 paper also reports σ(r) = 0.009 from simulations.27  No newer B-mode data have beaten it.  Reanalyses that add Planck's reprocessed maps, galaxy-survey distances and the newer Atacama and South Pole Telescope maps tighten the number only slightly:  r < 0.032 in 2022, and r < 0.034 at the end of 2025, which its authors call consistent with the BICEP/Keck result.2821

Planck's own limit from temperature and polarisation alone is r0.002 < 0.10, tightening to r0.002 < 0.056 when BICEP/Keck's 2015 data are added.16

Two experiments were supposed to settle this.  One of them no longer exists.  CMB-S4 was designed to reach σ(r) = 0.0005.  On 9 July 2025 the U.S. Department of Energy and the National Science Foundation issued a statement to the project saying "DOE and NSF have jointly decided that they can no longer support the CMB-S4 Project," and the project began an orderly shutdown.29  LiteBIRD, a JAXA satellite planned for launch in the late 2020s, remains.  Its stated full success criterion is δr < 0.001 for a universe with r = 0.30

BICEP2, and how a detection became dust

On 17 March 2014 the BICEP2 collaboration announced a detection.  The paper posted that day reported the B-mode signal as "well-fit by a lensed-LCDM + tensor theoretical model with tensor/scalar ratio r = 0.20 (+0.07, −0.05), with r = 0 disfavored at 7.0σ," and added that "subtracting the best available estimate for foreground dust modifies the likelihood slightly so that r = 0 is disfavored at 5.9σ."31  It was reported worldwide as the confirmation of inflation.

The signal was Galactic dust.

Here is how it came apart, and the sequence matters because it is a case study in a field correcting itself in under a year.

The dust models were guesses.  BICEP2 had no measurement of polarised dust in its own patch of sky.  Planck had the data and had not released it.  One of BICEP2's models, called DDM2, was built from numbers read off a slide in a Planck conference presentation.

Independent groups found the ambiguity within ten weeks.  Raphael Flauger, J. Colin Hill and David Spergel posted a reanalysis on 28 May 2014 and stated the problem exactly:  the data "are consistent with a cosmology with r = 0.2 and negligible foregrounds, but also with a cosmology with r = 0 and a significant dust polarization signal."32

BICEP2 corrected itself in print.  The version published in Physical Review Letters on 19 June 2014 dropped DDM2 and replaced the strong claim with a hedge:  the available dust models "are not sufficiently constrained by external public data to exclude the possibility of dust emission bright enough to explain the entire excess signal."31  An endnote explains why the model was withdrawn:

In the preprint version of this paper an additional DDM2 model was included based on information taken from Planck conference talks…  In the Planck dust polarization paper which has since appeared the maps have been masked to include only regions "where the systematic uncertainties are small, and where the dust signal dominates total emission."  This mask excludes our field.  We have concluded the information used for the DDM2 model has unquantifiable uncertainty.31

Planck measured the dust.  On 19 September 2014 the Planck collaboration published its own map of polarised dust emission at high latitude.  For the BICEP2 patch, extrapolated to BICEP2's observing frequency, the dust power was "comparable in magnitude to the BICEP2 measurements at these multipoles that correspond to the recombination bump."33  In other words, dust alone could account for the whole thing.

The joint analysis closed it.  BICEP2, Keck and Planck combined their data and posted the result on 2 February 2015.  The finding:  "We find strong evidence for dust and no statistically significant evidence for tensor modes…  yields an upper limit r0.05 < 0.12 at 95% confidence."34

Eleven months from announcement to retraction, driven by the collaboration's own data release and by outside groups who checked the work.

The right lesson is not that cosmology is unreliable.  It is that this particular measurement is very hard, that the foreground is at the same level as the signal, and that a future claimed detection of B-modes has to clear a bar this episode set.  Anyone using BICEP2 to sneer at the field should notice who found the error:  cosmologists, in public, in months.

Why no measurement of r can kill inflation

Here is the asymmetry that drives the whole falsifiability dispute.

A detection of primordial B-modes would be a spectacular confirmation of inflation.  A non-detection, at any level, confirms nothing and refutes nothing.

The reason is that the surviving model families can push r as low as you like.  The α-attractors are the clearest case.  Renata Kallosh, Andrei Linde and Diederik Roest showed in 2013 that a large class of models converges on ns = 1 − 2/N and r = 12α/N², where N is the number of e-folds and α is a free parameter set by the curvature of a geometry in the underlying supergravity theory.35  Take α smaller and r falls with it, while ns stays put at about 0.967 — exactly where Planck measures it.

Planck's 2018 analysis bounds α from above, at log10 α < 1.3 for one variant.16  There is no lower bound.  There cannot be one from a null result.

The model builders say this themselves, and the sentence is remarkable.  In the introduction to the same paper, Kallosh, Linde and Roest write that supergravity model-building "allows to provide a consistent supergravity interpretation of any possible set of the observational parameters ns and r."35

Any possible set.  That is the critics' entire case, stated by the architects, as a selling point.

Individual models do die, and it is worth quoting the exclusions in the collaborations' own careful wording rather than the popular version.  Planck 2013:  "Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n ≥ 2 do not provide a good fit to the data."36  Planck 2015:  "These results imply that V(φ) ∝ φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2 inflation."14  BK18:  "The φ2/3 model now lies outside the 95% contour as does the band of natural inflation models."27  That is genuine empirical content, and it is why the fairest description is that inflation as a framework is not falsifiable by r while inflation as a set of specific models is being narrowed steadily.

The strongest critique is internal

The hardest attack on inflation does not come from creationists, or from steady-state holdouts, or from philosophers.  It comes from Paul Steinhardt, who helped invent new inflation in 1982, working with Anna Ijjas and Abraham Loeb.

Their case has three parts.  Take them in order, because the third depends on the first two.

Part one: the models that fit are the models inflation says are unlikely

After Planck's 2013 data, the surviving inflation models were nearly all "plateau" models — potentials with a long flat shelf the field rolls along.  The simpler power-law shapes were being squeezed out.

Ijjas, Steinhardt and Loeb argued that this is worse for inflation than it looks, because inflation's own logic says plateau models are the improbable ones.  A power-law potential offers a far wider range of starting field values that lead to inflation, and produces far more expansion when it does.  So if you ask which kind of potential a random starting condition would land on, inflation itself answers:  the power-law kind.  The data say otherwise.

Obviously, 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.  The unlikeliness problem is an alarm warning us that a paradigm can fail even though observations favor a class of models if the paradigm predicts the class of models is unlikely.37

The data behind Part one have moved since 2013, and the move helps neither side cleanly.  With the microwave background alone, the 2025 numbers still sit within 2.0σ of Starobinsky's plateau model.  Adding the DESI galaxy survey's 2025 distances pushes ns up to 0.9728 ± 0.0029.  On that combination Starobinsky's prediction misses by 3.9σ, and the data favour a power-law potential with an exponent near 1/3.  The authors add a caution:  the 3.9σ is for the simplest form of the prediction at one chosen number of e-folds, and the details of how inflation ends can move Starobinsky's predicted ns.21  If the shift holds, it weakens the premise of Part one, because the data would no longer single out plateau models.  But the same paper carries a second lesson.  Its authors trace the shift to "marginally significant differences between the CMB and DESI data that remain unexplained," and add that "a class of polynomial α-attractor models can predict the CMB as well as the CMB+DESI ns results."21  One model family fits either answer by changing the number of e-folds.  That is the same flexibility the α-attractors show for r, described above, now applied to ns.

Part two: inflation needs the smoothness it was hired to produce

Plateau models need a large, smooth, low-curvature starting patch — larger than the patch a power-law model needs, by a lot.  The paper puts the requirement at "initial smoothness on the scale of a billion or more Hubble volumes."37  The conclusion is the circularity charge:

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!37

In the popular version they sharpen it to one sentence:

More important, 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.  Recall that the entire motivation for introducing it was to explain how the visible universe came to have these properties; if starting inflation requires those same properties, with the only difference being that a smaller patch of space is needed, that is hardly progress.38

Part three: eternal inflation destroys the predictions

This is the part that reaches the multiverse, and it is where the argument gets its teeth.

Once inflation starts, quantum fluctuations keep kicking the field back up the potential in some regions.  Those regions keep inflating.  They inflate faster than the regions that finish, so the inflating volume always dominates.  Inflation never ends globally; it only ends in pockets.  Guth's review states the technical position:  "inflation is generically eternal into the future."39  There is an irony here worth recording:  the same review credits the discovery to Steinhardt.  "The eternal nature of new inflation was first discovered by Steinhardt, and later that year Vilenkin showed that new inflationary models are generically eternal."39  The feature Steinhardt now says makes inflation untestable is one he found.

Guth also states the consequence, in a section headed "Difficulties in Calculating Probabilities":

In an eternally inflating universe, anything that can happen will happen; in fact, it will happen an infinite number of times.  Thus, the question of what is possible becomes trivial—anything is possible, unless it violates some absolute conservation law.  To extract predictions from the theory, we must therefore learn to distinguish the probable from the improbable.39

That last sentence is the whole of the measure problem.  To say a theory predicts something, you have to be able to say it is likely.  In an infinite ensemble where every outcome occurs infinitely often, saying which is likelier requires a rule for comparing infinities.  Such a rule is called a measure.  Different measures give different answers, and no one has found a principled reason to prefer one.

Ijjas, Steinhardt and Loeb draw the obvious conclusion:

inflationary cosmology, as we currently understand it, cannot be evaluated using the scientific method.  As we have discussed, the expected outcome of inflation can easily change if we vary the initial conditions, change the shape of the inflationary energy density curve, or simply note that it leads to eternal inflation and a multimess.  Individually and collectively, these features make inflation so flexible that no experiment can ever disprove it.38

Steinhardt's sharpest wording is his own, in Nature, on 3 June 2014, written in the aftermath of the BICEP2 collapse:  "it is clear that the inflationary paradigm is fundamentally untestable, and hence scientifically meaningless."40

The multiverse this produces has its own article.  What matters here is only the logic:  eternal inflation is not an optional add-on.  It falls out of the same models that fit the data, and it is what makes the measure problem unavoidable.

The reply, and the exchange in Scientific American

In January 2017 Ijjas, Steinhardt and Loeb published "Pop Goes the Universe" in Scientific American.  On 10 May 2017 thirty-three physicists replied in the same magazine's blog under the title "A Cosmic Controversy."  The signatories include Guth, Linde, David Kaiser, Yasunori Nomura, 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, John Mather, Hiranya Peiris, Rainer Weiss and Matias Zaldarriaga.14

This is the sharpest published statement of both positions.  It is short.  Read both.

The reply's core argument is that inflation has been tested, repeatedly, and passed.

An important point is that standard inflationary models could have failed any of the empirical tests described above, but they did not.  IS&L write about how "a failing theory gets increasingly immunized against experiment by attempts to patch it," insinuating that this has something to do with inflation.  But despite IS&L's rhetoric, it is standard practice in empirical science to modify a theory as new data come to light, as, for example, the Standard Model has been modified to account for newly discovered quarks and leptons.  For inflationary cosmology, meanwhile, there has so far been no need to go beyond the class of standard inflationary models.14

On the multiverse, the reply separates two questions:

IS&L also assert that inflation is untestable because it leads to eternal inflation and a multiverse.  Yet although the possibility of a multiverse is an active area of study, this possibility in no way interferes with the empirical testability of inflation.  If the multiverse picture is valid, then the Standard Model would be properly understood as a description of the physics in our visible universe, and similarly the models of inflation that are being refined by current observations would describe the ways inflation can happen in our particular part of the universe.14

And they invoke the size of the field:

According to the high-energy physics database INSPIRE, there are now more than 14,000 papers in the scientific literature, written by over 9,000 distinct scientists, that use the word "inflation" or "inflationary" in their titles or abstracts.  By claiming that inflationary cosmology lies outside the scientific method, IS&L are dismissing the research of not only all the authors of this letter but also that of a substantial contingent of the scientific community.14

Ijjas, Steinhardt and Loeb answered in the same posting:

Our point is that we should be talking about the contemporary version of inflation, warts and all, not some defunct relic.  Logically, if the outcome of inflation is highly sensitive to initial conditions that are not yet understood, as the respondents concede, the outcome cannot be determined.  And if inflation produces a multiverse in which, to quote a previous statement from one of the responding authors (Guth), "anything that can happen will happen"—it makes no sense whatsoever to talk about predictions.  Unlike the Standard Model, even after fixing all the parameters, any inflationary model gives an infinite diversity of outcomes with none preferred over any other.  This makes inflation immune from any observational test.14

Scoring the exchange

Some parts of this can be judged from the record.

The reply is right that tests happened and could have failed.  The tilt could have come out at 1.00 or above 1.  The perturbations could have been isocurvature, or strongly non-Gaussian.  Ω could have settled at 0.3.  None of those happened.  That is empirical content, and Steinhardt's "scientifically meaningless" overstates it.

The critics are right that no one has solved the measure problem, and the reply concedes it.  Guth, Kaiser and Nomura, in the paper that answers the 2013 version of this argument:  "although significant progress has been made in recent years, a persuasive theory of probabilities in the multiverse has not yet been found."41  And, in the same paper, a sentence that gives away more than it looks:

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.41

That is a policy under which the paradigm cannot lose.  Confirmations count for inflation; disconfirmations count against our understanding of the measure.  Guth, Kaiser and Nomura are not being evasive — they say plainly that the measure problem "is simply an important problem that remains to be solved," and they point out that Steinhardt's own cyclic models have one too.41  But the asymmetry is real and a reader should see it.

The appeal to 14,000 papers is the weakest thing in the reply.  Whether a theory is testable is not settled by how many people work on it.  Both sides in the exchange complain about arguments from authority, and only one side makes one.

Both sides agree on more than the tone suggests.  Both agree that plateau models fit the microwave-background data;  the 2025 galaxy-survey numbers have reopened that, as Part one notes.  Both agree that eternal inflation follows from those models.  Both agree that no one can compute probabilities in the resulting ensemble.  The disagreement is about what to call a theory in that condition.

Penrose's version, which is deeper than either

Roger Penrose makes an objection that neither side in the Scientific American exchange addresses, and it is worth stating because it does not depend on measures at all.

Inflation is supposed to smooth the universe.  Smoothing is an entropy-increasing process.  Any entropy-increasing process runs only because it started from a lower-entropy state.  So inflation cannot explain why the early universe had low entropy, because it consumed that low entropy to do its job.

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.42

Penrose is careful about the scope of his own argument and this article will be too.  He writes that his 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," and adds that "inflationists have made some definite predictions which, in recent years, have measured up remarkably well."42

Andreas Albrecht, who co-authored one of the two new-inflation papers in 1982, conceded the point in print twenty years later:  "inflation does not predict the arrow of time.  Inflation 'passes the arrow of time buck' to the special initial conditions of the inflaton field."43

One caution about using this in an apologetic argument.  Penrose's number for the improbability of the initial state, 1 in 10 to the power 10123, is a ratio of phase-space volumes computed with a measure.  The Berean Archive's fine-tuning article declines to treat such measures as objective chances, for reasons that apply here as much as there.  An argument cannot reject the measure when a skeptic uses one and accept it when an apologist does.  Penrose's qualitative point — that a smoothing mechanism presupposes what it is meant to explain — survives without any measure, and that is the form this article uses.

What a Christian should make of it

Inflation is neither an argument for creation nor an argument against it.  It is a proposed mechanism inside a model of the deep past.  Whether the universe went through a burst of accelerated expansion at 10−34 seconds has no bearing on whether it was made, and a reader who came here looking for either conclusion should be told that plainly.

What follows is about how the argument is misused in both directions.

Do not use it as evidence for the Bible

The clearest case is Hugh Ross's 2015 article "Cosmic Inflation: It Really Happened."  From the South Pole Telescope's measurement of ns = 0.9593 ± 0.0067, Ross computed the distance from 1 in standard deviations and converted it into a probability:

The SPT team proved the reality of cosmic inflation to 6.075 standard deviations—(1.0 – 0.9593)/0.0067…  In light of the team's measurements, we now can be 99.9999999 percent certain that the universe indeed went through an inflation event when the universe was only about 10−34 seconds old.44

That is not what the number means.  The 6.075σ measures how far ns sits from 1.  Converting it into a probability that inflation occurred requires the extra premise that only inflation can produce ns < 1, and Ross states that premise:  "For a universe with no inflation event, ns equals 1.0 or greater."44  It is false.  Harrison and Zel'dovich got ns = 1 with no inflation at all, and the ekpyrotic and bouncing models Steinhardt works on produce tilted spectra too.  The measurement narrows the field.  It does not close it.

John Hartnett of Creation Ministries International answered Ross the following month and got this part right:

Now the claim of proof that the inflation event really happened hinges on the value of ns.  But what requires that that number must be less than unity to 'prove' inflation really occurred?  The modelling does.45

He also noticed that Planck had published a nearly identical value in 2013 — ns = 0.9603 ± 0.0073 — and that nobody claimed to have proved inflation then.45

Ross's second claim is theological:  that the confirmation is "good news for Christians because for more than 2,500 years the Bible and biblical commentaries were the only books proclaiming the fundamental features of big bang cosmology," including "ongoing expansion since that beginning," citing Isaiah 40:22 and ten other verses.44  Hartnett's reply is the right one and it is exegetical, not scientific:  Isaiah 40:22 says the heavens are stretched out "as a curtain" and spread "as a tent."  Those are similes, and a simile carries its own limit.  A tent stretches by a few percent.45

An apologetic that reads modern cosmology out of ancient Hebrew tent imagery will not survive contact with a reader who knows either.

The creationist critique has picked the right floor

Michael Disney, an astronomer at Cardiff and no creationist, described big bang cosmology as five theories stacked on each other:  Expansion on the ground floor, then Inflation, then Dark Matter, then the density seeds, then Dark Energy.46  Creationist writers who single out inflation as the weakest load-bearing layer have identified the right floor.  Inflation is the layer with no direct observational signature of its own, no accepted model, and an unsolved probability problem at its foundation.

But the reasons usually given are imprecise, and three of them should be dropped.

"Inflation was invented to fix a problem, so it is ad hoc."  Half right.  It was invented to fix a problem — Guth says so in his title.  But inventing a mechanism to fix a problem is normal physics, and what matters is whether the mechanism then makes new predictions that could have failed.  Inflation did:  the tilt.  It came out right.  An argument that stops at "ad hoc" has not engaged the strongest thing on the other side.

"Inflation requires faster-than-light expansion."  John Hartnett's Creation article calls it "faster-than-light inflation" four times and lists it among the big bang's "fudge factors":  "Big bang cosmogony requires many fudge factors to stay afloat, including dark matter, dark energy, and faster-than-light inflation."47  This is not an objection.  General relativity places no speed limit on the expansion of space itself, only on signals moving through it, and the same is true of ordinary Hubble expansion at large distances today.  A young-earth reader should be especially careful here, because several young-earth cosmologies rely on exactly the same feature of general relativity.

"Flatness."  The same article recites the standard version as fact:  "This is a cosmological fine-tuning problem, where the force of the expansion matched the force of gravity to one part in 1060."47  That is the argument Helbig calls "completely bogus" in MNRAS and Carroll and Tam call "an illusion."  A critic who leans on it is borrowing a claim that mainstream cosmologists have already taken apart, and a well-read skeptic will say so.

"Monopoles."  Repeating the monopole problem treats an unobserved grand unified theory as though it were established physics.  It is the weakest of the three and should be dropped from creationist lists.

One thing in Hartnett's article is right and worth keeping.  He writes that "there is no good mechanism to cause this faster-than-light expansion, or to stop it once it began."47  The second half is a fair description of Guth's 1981 model, which Guth himself abandoned for exactly that reason.  It is not a fair description of slow-roll models, where the field simply reaches the bottom of its potential.  Half a point.

What the honest critique actually is

Four things, all of which come from inside the field.

  1. Thirty years of searching has not found the signature. r0.05 < 0.036, and no finite improvement on that number can settle the question either way.
  2. No one can compute a probability in an eternally inflating universe. Guth, Kaiser and Nomura say so: "a persuasive theory of probabilities in the multiverse has not yet been found."41
  3. The mechanism regresses to the conditions it was hired to explain. Ijjas, Steinhardt and Loeb on initial conditions; Carroll and Tam on Liouville's theorem; Penrose and Albrecht on entropy.
  4. Guth's own paper asked for something better and nobody has produced it. "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."1

That is a strong enough case that it does not need help from the weak arguments.

And the cost, stated plainly

A young-earth reader who rejects inflation has to say something about ns = 0.9649 ± 0.0042.  It is a number nobody had measured when it was predicted; it is eight standard deviations from the value the pre-inflation theory gave; and it is on the side and of the size that inflation requires.  "The model is wrong so the number means nothing" is not an answer, because the number was predicted before it was measured.

The honest position is that this article's own framework — that the big bang is a stack of separable claims — cuts both ways.  Inflation is the floor with the least direct support.  It is also the floor that produced the one clean advance prediction in the whole stack that was confirmed after the fact rather than fitted.

One thing inflation does not do

It does not remove the need for a beginning.  Arvind Borde, Guth and Alexander Vilenkin proved in 2003 that an expanding spacetime cannot be extended indefinitely into the past, and their theorem needs no energy condition, which is what makes it apply to inflating spacetimes at all.  Their own conclusion:  "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."48

Do not over-read it.  Guth denies that it establishes a unique beginning:  "There is of course no conclusion that an eternally inflating model must have a unique beginning."49  Vilenkin is equally direct, and both halves of what he says have to travel together:  "The answer to the question, 'Did the universe have a beginning?' is, 'It probably did.'"  And, two sentences later:  "my own view is that the theorem does not tell us anything about the existence of God."50  Quoting either man's half-sentence in a creation argument is quote-mining, and this project does not do it.  The theorem is treated properly in the standard model overview.

Objections and responses

"Inflation has been confirmed.  Planck said so."  Planck's inflation paper says its findings "support the key predictions of the standard single-field inflationary models."16  That is the right wording and it is narrower than "confirmed."  What is confirmed is a set of statistical properties — flatness, near-scale-invariance with a red tilt, adiabaticity, Gaussianity — that the standard inflationary models predict.  Bouncing and ekpyrotic models also produce super-horizon fluctuations, as the WMAP discovery paper itself noted.26  And the signature that would pick inflation out uniquely, primordial B-modes, has not been seen.

"Steinhardt is a disgruntled outsider."  He is not.  He co-authored one of the two 1982 papers that made inflation work at all, and Guth's own review credits him with discovering eternal inflation.939  His critique is not that inflation is unmotivated; it is that the version now known to be correct has properties that make it untestable.

"Thirty-three eminent physicists signed a rebuttal, so the critique must be wrong."  Counting signatures is not evidence, and the letter's own weakest passage is its appeal to "more than 14,000 papers…  written by over 9,000 distinct scientists."14  The letter's real argument is the list of tests inflation passed, and that argument stands on its own without the roster.

"BICEP2 shows cosmologists will believe anything."  It shows the opposite.  BICEP2 announced on 17 March 2014, was challenged in print by ten weeks, hedged its own published version by June, withdrew its dust model in an endnote, and was closed out by a joint analysis with the group holding the better data within eleven months.323134  That is how error correction is supposed to look.

"If inflation is unfalsifiable, it is not science."  Careful.  Steinhardt's Nature wording — "fundamentally untestable, and hence scientifically meaningless" — goes further than his own published arguments support.  Specific inflationary models are excluded regularly:  Planck 2013 found monomial potentials of degree n ≥ 2 a poor fit, Planck 2015 called φ2 and natural inflation disfavoured, and BK18 put φ2/3 and natural inflation outside the 95% contour.361427  The honest statement is narrower and harder to dismiss:  the framework is not falsifiable by any measurement of r, because the model space extends continuously to r = 0.

"Inflation solved the horizon problem, so the horizon problem is not evidence for anything."  Inflation relocates the horizon problem into a requirement on the pre-inflationary state.  Carroll and Tam:  "Inflation by itself cannot solve the horizon problem, in the sense of making the smooth early universe a natural outcome of a wide variety of initial conditions."2  That said, this article does not run the horizon problem as evidence for creation either, for the same reason the fine-tuning article does not:  it is a claim about how likely an initial condition was, and this project has declined to treat measures over initial conditions as objective chances.

"The big bang has its own light-travel-time problem, so young-earth cosmology is no worse off."  This is a bad argument and should be retired.  The horizon problem asks why two regions that never communicated have the same temperature.  Nothing had to travel anywhere; the model merely fails to explain a correlation.  The young-earth starlight problem requires photons actually to have crossed billions of light years in thousands of years.  Those are different logical shapes, and any cosmologist will see the difference immediately.  The young-earth answers are surveyed in young-earth cosmologies.

"Nothing has improved on r < 0.036 in five years, so the field has given up."  The field lost its main instrument.  CMB-S4, designed for σ(r) = 0.0005, had its joint DOE and NSF support withdrawn on 9 July 2025.29  LiteBIRD is still planned, with a stated goal of δr < 0.001.30  The question is open, not abandoned.

What would settle it

Inflation is unusual among the disputes in this corpus because both sides agree on what the decisive measurement would be.

A detection of primordial B-modes would essentially settle it in inflation's favour.  Nothing else known produces gravitational waves at that wavelength and amplitude.  A clean detection at, say, r = 0.01, with the right spectral shape and the right consistency relation between the tensor tilt and r, would leave the critics with very little.  LiteBIRD is built to reach δr < 0.001.

A non-detection settles nothing, and this is the asymmetry the whole argument turns on.  The α-attractors extend continuously to r = 0.  There is no value of r low enough to exclude inflation as a class.

A solution to the measure problem would change the argument on both sides.  If someone finds a principled measure on eternally inflating spacetimes, inflation regains the ability to make predictions and the strongest form of the Steinhardt critique dissolves.  If it is proven that no such measure exists, the critique becomes decisive.  Neither has happened, and both sides say so.

A worked-out bouncing cosmology that reproduces the observed spectrum would give the field a real alternative.  Justin Khoury, Burt Ovrut, Steinhardt and Neil Turok proposed the ekpyrotic model in 2001, in which the hot big bang comes from a brane collision "beginning from an otherwise cold, vacuous, static universe," and which "addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations."51  It is a minority programme with its own unsolved problems, but it is not vapour, and the fact that a live rival exists is itself evidence that the horizon problem is a puzzle rather than a crisis.

Eternal inflation has already been tested once, and the test came back null.  If our bubble collided with another, the scar should show in the microwave background.  Stephen Feeney, Matthew Johnson, Daniel Mortlock and Hiranya Peiris ran the search on WMAP's seven-year data and reported that the data "do not warrant augmenting ΛCDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky N̄s < 1.6 at 68% CL."52  A null result on one particular signature is not a refutation of the multiverse, but it does show that the picture is not wholly beyond reach of data — a point that cuts against the strongest form of the untestability charge.  See the multiverse article.

Until then, the accurate description is the one this article has argued for throughout:  inflation is a well-motivated framework with one clean confirmed prediction, one missing signature, and an unsolved problem at its foundation that its own architects acknowledge in print.

Sources


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    Guth, Alan H.  “Inflationary universe: A possible solution to the horizon and flatness problems.”  Physical Review D 23:347–356.  1981.  Alan H. Guth's journal paper, whose title proposes inflation as a possible solution to the horizon and flatness problems.  The article uses it for those two problems, and for Guth's own figures on how finely the starting conditions would have had to be tuned. ↩

    1. 1a.

      Section I, Introduction:  “consists of at least 083 separate regions which are causally disconnected (i.e., these regions have not yet had time to communicate with each other via light signals)…  Thus, one must assume that the forces which created these initial conditions were capable of violating causality.”  The figure is for an assumed initial temperature T0 = 1017 GeV. ↩

    2. 1b.

      Section I, Introduction:  “For the initial conditions taken at T0 = 1017 GeV, the value of H0 must be fine tuned to an accuracy of one part in 1055.”  And, for a lower starting temperature:  “If I had chosen a modest value like T0 = 1 MeV, I would still have concluded that the 'initial' universe consisted of at least 022 causally disconnected regions, and that the initial value of H0 was fine tuned to one part in 1015.” ↩ ↩

    3. 1c.

      Section IV, Grand Unified Models and Magnetic Monopole Production:  “far too many monopoles would be produced.  Thus, the monopole problem…” ↩

    4. 1d.

      Section V, Problems of the Inflationary Scenario:  “As I mentioned earlier, the inflationary scenario seems to lead to some unacceptable consequences.  It is hoped that some variation can be found which avoids these undesirable features, but maintains the desirable ones.” ↩

    5. 1e.

      Section V:  “The central problem is the difficulty in finding a smooth ending to the period of exponential expansion…  The randomness of the bubble formation process then leads to gross inhomogeneities.” ↩

    6. 1f.

      Section VI:  The closing sentence.  “In conclusion, the inflationary scenario seems like a natural and simple way to eliminate both the horizon and the flatness problems.  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.” ↩ ↩

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    Carroll, Sean M., and Heywood Tam.  “Unitary Evolution and Cosmological Fine-Tuning.”  arXiv preprint.  2010.  A 2010 preprint by Sean M. Carroll and Heywood Tam of the California Institute of Technology.  It uses the invariant measure on solutions to Einstein's equation to quantify cosmological fine-tuning, and it finds that the flatness problem is an illusion while the horizon problem is real.  The article uses it because the authors argue that inflation moves the horizon problem back into the starting conditions rather than solving it, though they still think inflation is worth having.

    1. 2a.

      Section §6, Discussion:  “Using the invariant measure on cosmological solutions to Einstein's equation, we find that the flatness problem is an illusion; in the context of purely Robertson-Walker cosmologies, the measure diverges on flat universes.” ↩

    2. 2b.

      Section §6, Discussion:  “Inflation by itself cannot solve the horizon problem, in the sense of making the smooth early universe a natural outcome of a wide variety of initial conditions.” ↩ ↩

    3. 2c.

      Section Abstract:  “The most natural interpretation of the measure is the flatness problem does not exist; almost all Robertson-Walker cosmologies are spatially flat.  The homogeneity of the early universe, however, does represent a substantial fine-tuning; the horizon problem is real.”  Section §5.2:  The same sentence appears at the end of §5.2:  “the observed homogeneity of our universe does imply considerable fine-tuning; unlike the flatness problem, the horizon problem is real.” ↩

    4. 2d.

      Section Abstract:  On inflation, the abstract says:  “nevertheless provides an appealing target for true theories of initial conditions, by allowing for small patches of space with sub-Planckian curvature to grow into reasonable universes.”  Section §5.3:  The paper computes, at eq. (100):  “P(inflation) ≈ (10−66)n ≈ 10−66,000,000”.  That is, 10 raised to the power −6.6 × 107. ↩

  3. 3.

    Helbig, Phillip.  “Is there a flatness problem in classical cosmology?”  Monthly Notices of the Royal Astronomical Society 421(1):561–569.  2012.  A paper by a single author that reviews the flatness problem and works out new calculations for models of the universe that will collapse in the future.  It concludes that the flatness problem does not exist for any model in the standard family of expanding-universe models.  The article cites it as a critic of the flatness argument.

    1. 3a.

      The paper describes the standard flatness argument as.  “completely bogus.” ↩

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    Lewis, Geraint F., and Luke A. Barnes.  A Fortunate Universe: Life in a Finely Tuned Cosmos.  Cambridge University Press.  2016.  A book for general readers by two researchers at the Sydney Institute for Astronomy, surveying physics from particles and forces up to galaxies and asking whether the universe is fine-tuned for life.  The authors argue that it is, and they weigh chance, a multiverse and design as explanations.  The article uses it because its authors, who argue for fine-tuning, concede a point about flat universes.

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      Page 180:  On flatness: the Hawking-Page measure gives flat universes measure 100%.  “flat universes are utterly unsurprising.” ↩

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    Super-Kamiokande Collaboration.  “Search for proton decay via p → e+π0 and p → µ+π0 with an enlarged fiducial volume in Super-Kamiokande I-IV.”  Physical Review D 102:112011.  2020.  A search for proton decay in Super-Kamiokande data, with an enlarged fiducial volume.  It sets lower limits on the proton's lifetime in two decay channels.  The first author is A. Takenaka.  The article uses its limit to show that every simple grand unified model that predicted faster decay is ruled out.

    1. 5a.

      Section Abstract:  “We set lower limits on the partial lifetime for each of these modes:  τ/B(p → e+π0) > 2.4 × 1034 years and τ/B(p → µ+π0) > 1.6 × 1034 years at 90% confidence level.” ↩

  6. 6.

    Guth, Alan H., and Erick J. Weinberg.  “Could the Universe Have Recovered from a Slow First Order Phase Transition?”  Nuclear Physics B 212:321–364.  1983.  A general proof, by Alan H. Guth and Erick J. Weinberg, that Guth's original mechanism cannot end gracefully.  Its title asks whether the universe could recover from a slow first-order phase transition, a change of state that happens through bubbles, and the article reads the answer as no.  The article uses it for the graceful exit problem: bubbles must form slowly or inflation stops too soon, yet slowly forming bubbles never merge into a smooth universe. ↩

  7. 7.

    Linde, Andrei.  Inflationary Cosmology after Planck 2013.  2014.  A long review of inflation, written up from lectures given at the Les Houches summer school in 2013 by a Stanford physicist.  It surveys inflation's status after the 2013 Planck data and gives special attention to a new family of models called cosmological attractors.  The article quotes it as an insider's own admissions: that the early scenarios failed, and that inflation models struggled before dark energy was discovered.

    1. 7a.

      Section §11, "Inflation and observations":  “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.” ↩

    2. 7b.

      Section §2, "Brief history of inflation":  “If the probability of the bubble formation is large, bubbles of the new phase are formed near each other, inflation is too short to solve any problems, and the bubble wall collisions make the universe extremely inhomogeneous.  If they are formed far away from each other, which is the case if the probability of their formation is small and inflation is long, each of these bubbles represents a separate open universe with a vanishingly small Ω.  Both options are unacceptable, which has lead to the conclusion that this scenario does not work and cannot be improved (graceful exit problem).” ↩

    3. 7c.

      Section §2:  “In most versions of this scenario the inflaton field must have an extremely small coupling constant, so it could not be in thermal equilibrium with other matter fields, as required…  This means that new inflation could explain why our universe was so large only if it was very large and contained many particles from the very beginning.” ↩

    4. 7d.

      Section §2:  “This idea was abandoned by all experts actively working in this area of physics, but unfortunately it is still present in virtually all textbooks on astrophysics, which incorrectly describe inflation as an exponential expansion in a supercooled false vacuum state during the cosmological phase transitions in grand unified theories.” ↩

    5. 7e.

      Section §11:  “Many years ago, critics of inflation argued that the prediction ns = 1 is trivial because it was made by Harrison and Zeldovich (albeit without any real physical motivation) long before inflation.  Now the Harrison-Zeldovich spectrum is ruled out at the 5σ level, and inflationary expectations are confirmed.” ↩ ↩

  8. 8.

    Linde, Andrei D.  “A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems.”  Physics Letters B 108:389–393.  1982.  A physics paper that proposes a new inflationary scenario as a possible solution to the horizon, flatness, homogeneity, isotropy and primordial monopole problems.  The article uses it as the origin of the first fix for the horizon problem, which Albrecht and Steinhardt reached independently three months later. ↩

  9. 9.

    Albrecht, Andreas, and Paul J. Steinhardt.  “Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking.”  Physical Review Letters 48:1220–1223.  1982.  One of the two papers that introduced new inflation, published three months after Linde's.  The article uses it to show that Steinhardt, the critic it answers, co-wrote one of those two papers. ↩ ↩

  10. 10.

    Linde, Andrei D.  “Chaotic Inflation.”  Physics Letters B 129:177–181.  1983.  A physics paper that describes chaotic inflation, the model class from which nearly all modern inflationary model-building descends.  The article uses it to show that Linde dropped the 1982 framework for a simpler model, a single scalar field that starts at a large value somewhere. ↩

  11. 11.

    Martin, Jérôme et al.  “Encyclopædia Inflationaris.”  Physics Reports 528:1–192.  2013.  An encyclopaedia of inflationary models, the reference work the article uses to count how many models have been worked out.  The Opiparous Edition is version 5 of the same arXiv entry, dated 17 December 2024.  The article uses it for the count, from 64 models in 2013 to 118 in 2024.

    1. 11a.

      Abstract of v1 (15 March 2013), on ASPIC, the authors' software:  “has been designed as an evolutive code which presently supports 64 different models, a number that may be compared with three or four representing the present state of the art.” ↩

    2. 11b.

      Abstract of v5, the Opiparous Edition (17 December 2024):  “This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios…  ASPIC has been designed as an evolutive code which presently supports 118 different models.” ↩

  12. 12.

    Martin, Jérôme et al.  “Vanilla Inflation Predicts Negative Running.”  EPL 148:29002.  2024.  A physics paper that computes a probability distribution over nearly 300 single-field slow-roll models of inflation, using the latest cosmological data.  The article cites it for the size of the model space its analysis covers, nearly 300 models.

    1. 12a.

      Section Abstract:  “Using latest cosmological data, we compute its marginalized posterior probability distribution over the space of nearly 300 models of single-field slow-roll inflation.” ↩

  13. 13.

    Martin, Jérôme et al.  “The Best Inflationary Models After Planck.”  Journal of Cosmology and Astroparticle Physics 2014(03):039.  2014.  A statistical study that scores 193 slow-roll models of inflation against the 2013 Planck data.  It uses Bayesian evidence, a score for how well a model fits the data, and Bayesian complexity, a penalty for models that need more settings; with complexity included, only 9 potential shapes are preferred.  The article uses it to show that the models the data favor are all plateau-shaped.

    1. 13a.

      Section Abstract:  “We compute the Bayesian evidence and complexity of 193 slow-roll single-field models of inflation using the Planck 2013 Cosmic Microwave Background data…  Our analysis singles out the most probable models (from an Occam's razor point of view) that are compatible with Planck data, while ruling out with very strong evidence 34% of the models considered.  We identify 26% of the models that are favoured by the Bayesian evidence, corresponding to 15 different potential shapes.  If the Bayesian complexity is included in the analysis, only 9% of the models are preferred, corresponding to only 9 different potential shapes.  These shapes are all of the plateau type.” ↩

  14. 14.

    Planck Collaboration.  “Planck 2015 results. XX. Constraints on inflation.”  Astronomy & Astrophysics 594:A20.  2016.  The inflation paper of the Planck satellite team, posted as arXiv:1502.02114, using the full mission's temperature data and the first release of polarization data on large angular scales.  It measures the spectral index of the primordial ripples as ns = 0.968 ± 0.006, and its upper bound on the tensor-to-scalar ratio, r, is below 0.11 at the 95% confidence level.  The article uses it for the paper's exclusion of the V(φ) ∝ φ2 model and natural inflation.

    1. 14a.

      Guth, Alan H., David I. Kaiser, Andrei D. Linde, Yasunori Nomura, and 29 co-signatories.  "A Cosmic Controversy."  Scientific American, 10 May 2017.  Full signatory list includes Charles Bennett, J. Richard Bond, François Bouchet, Sean Carroll, George Efstathiou, Stephen Hawking, Renata Kallosh, Eiichiro Komatsu, Lawrence Krauss, David Lyth, Juan Maldacena, John Mather, Hiranya Peiris, Malcolm Perry, Lisa Randall, Martin Rees, Misao Sasaki, Leonardo Senatore, Eva Silverstein, George Smoot, Alexei Starobinsky, Leonard Susskind, Michael Turner, Alexander Vilenkin, Steven Weinberg, Rainer Weiss, Frank Wilczek, Edward Witten and Matias Zaldarriaga.  https://www.scientificamerican.com/blog/observations/a-cosmic-controversy/. ↩

    2. 14b.

      From the 2017 open 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.)” ↩

    3. 14c.

      From the 2017 open letter.  “The standard inflationary models predict that the universe should have a critical mass density (that is, it should be geometrically flat), and they also predict the statistical properties of the faint ripples that we detect in the cosmic microwave background (CMB).  First, the ripples should be nearly 'scale-invariant'…  Second, the ripples should be 'adiabatic'…  Third, they should be 'Gaussian'…  Fourth and finally, the models also make predictions for the patterns of polarization in the CMB, which can be divided into two classes, called E-modes and B-modes.” ↩

    4. 14d.

      From the 2017 open letter.  “In 2016 the Planck satellite team (a collaboration of about 260 authors) summarized its conclusions by saying that 'the Planck results offer powerful evidence in favour of simple inflationary models.'”  Citation trap: that sentence is in Planck 2015 results XIII, Cosmological parameters (arXiv:1502.01589), not in Planck 2015 results XX, Constraints on inflation (arXiv:1502.02114). ↩

    5. 14e.

      From the 2017 open letter.  “An important point is that standard inflationary models could have failed any of the empirical tests described above, but they did not…  For inflationary cosmology, meanwhile, there has so far been no need to go beyond the class of standard inflationary models.” ↩

    6. 14f.

      From the 2017 open letter.  “IS&L also assert that inflation is untestable because it leads to eternal inflation and a multiverse.  Yet although the possibility of a multiverse is an active area of study, this possibility in no way interferes with the empirical testability of inflation.”  IS&L are Ijjas, Steinhardt and Loeb, the critics whom the letter answers. ↩

    7. 14g.

      From the 2017 open letter.  “According to the high-energy physics database INSPIRE, there are now more than 14,000 papers in the scientific literature, written by over 9,000 distinct scientists, that use the word 'inflation' or 'inflationary' in their titles or abstracts.” ↩ ↩

    8. 14h.

      Ijjas, Steinhardt and Loeb's reply, printed under "THE AUTHORS REPLY" in the same posting:  “Logically, if the outcome of inflation is highly sensitive to initial conditions that are not yet understood, as the respondents concede, the outcome cannot be determined.  And if inflation produces a multiverse in which, to quote a previous statement from one of the responding authors (Guth), 'anything that can happen will happen'—it makes no sense whatsoever to talk about predictions.  Unlike the Standard Model, even after fixing all the parameters, any inflationary model gives an infinite diversity of outcomes with none preferred over any other.  This makes inflation immune from any observational test.” ↩

    9. 14i.

      The arXiv preprint of this paper, arXiv:1502.02114.

    10. 14j.

      Section Abstract:  “These results imply that V(φ) ∝ φ2 and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as R2 inflation.” ↩ ↩

  15. 15.

    de Bernardis, P. et al.  “A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation.”  Nature 404:955–959.  Apr 27, 2000.  A Nature report from the BOOMERanG collaboration, whose balloon-borne telescope was flown over Antarctica and reported the first images of resolved structure in the cosmic microwave background over a significant part of the sky.  Its angular power spectrum has a peak at multipole 197 ± 6, which the authors say is consistent with a flat, Euclidean universe and strongly supports inflation.  The article uses it as the decisive measurement of flatness, nineteen years after the prediction.  Mirror:  arXiv

    1. 15a.

      “Marginalizing over all the other parameters, we found the following 95% confidence interval for Ω0 = Ωm + ΩΛ:  0.88 < Ω0 < 1.12.  This provides evidence for a euclidean geometry of the Universe.” ↩

  16. 16.

    Planck Collaboration.  “Planck 2018 results. X. Constraints on inflation.”  Astronomy & Astrophysics 641:A10.  2020.  The collaboration's analysis of what its 2018 measurements of the cosmic microwave background mean for cosmic inflation.  It reports results consistent with the two earlier Planck releases, with smaller uncertainties.  The article uses it for the spectral index, the flatness of the universe, the adiabatic test and the paper's own summary sentence.

    1. 16a.

      Section Abstract:  “Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be ns = 0.9649 ± 0.0042 at 68 % CL…  The Universe is found to be consistent with spatial flatness with a precision of 0.4 % at 95 % CL by combining Planck with a compilation of BAO data.  The Planck 95 % CL upper limit on the tensor-to-scalar ratio, r0.002 < 0.10, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain r0.002 < 0.056.” ↩ ↩ ↩

    2. 16b.

      Section Abstract:  “In correlated, mixed adiabatic and isocurvature models, the non-adiabatic contribution to the observed CMB temperature variance is constrained to 1.3 %, 1.7 %, and 1.7 % at 95 % CL for cold dark matter, neutrino density, and neutrino velocity, respectively.” ↩

    3. 16c.

      Section Abstract:  The final sentence.  “All these findings support the key predictions of the standard single-field inflationary models, which will be further tested by future cosmological observations.” ↩ ↩

    4. 16d.

      Section 4:  “Planck and BK15 data set tight constraints on α attractors.  We obtain log10 αE1 < 1.3 and log10 αE2 < 1.1 at 95 % CL for the E-model.  We obtain slightly tighter 95 % CL bounds for the T-model.”  These are upper bounds on α;  the paper states no lower bound. ↩

  17. 17.

    Bucher, Martin et al.  “An open universe from inflation.”  Physical Review D 52:3314–3337.  1995.  A 1995 paper, one of the models Linde describes as built to accommodate Ω ≈ 0.3.  The article uses it to show that these models are real, published and citable, not hypothetical. ↩

  18. 18.

    Linde, Andrei D., and Arthur Mezhlumian.  “Inflation with Ω ≠ 1.”  Physical Review D 52:6789–6804.  1995.  A physics paper on inflation in a universe whose density parameter Ω is not 1, so that space is not exactly flat.  The article cites it, along with a 1995 paper by Bucher, Goldhaber and Turok, as proof that inflation models for a non-flat universe were actually published. ↩

  19. 19.

    Mukhanov, Viatcheslav.  Quantum Cosmological Perturbations: Predictions and Observations.  2013.  A theory preprint by a single author that asks what the theory of quantum fluctuations predicts for inflation whatever the particular model.  Its abstract says the spectral index should deviate from flat by at least 3 percent, and that a lower bound follows on the gravitational waves produced.  The article uses it for the admission that inflation's flatness prediction was confirmed only after dark energy was discovered, when earlier data disagreed with it.

    1. 19a.

      On the flatness prediction, the author writes.  “This prediction was first confirmed only at the end of 90th with the discovery of dark energy.  Note that the experimental data before were in strong disagreement with it.” ↩

  20. 20.

    Planck Collaboration.  “Planck 2018 results. VI. Cosmological parameters.”  Astronomy & Astrophysics 641:A6.  2020.  The collaboration's full-mission results for the standard six-parameter model of the universe, fitted to the cosmic microwave background data (temperature, polarization and lensing).  Its spectral index, which says how the size of the early fluctuations changes with scale, is the value the article uses.

    1. 20a.

      ns = 0.9649 ± 0.0042, which the paper notes is 8σ from scale invariance. ↩

  21. 21.

    Balkenhol, L. et al.  “Inflation at the End of 2025: Constraints on r and ns Using the Latest CMB and BAO Data.”  The Open Journal of Astrophysics 9.  2026.  A short analysis that combines every major microwave-background data set available at the end of 2025 (Planck, the Atacama Cosmology Telescope's sixth data release, SPT-3G and BICEP/Keck), with and without DESI's 2025 galaxy-survey distances.  It finds ns = 0.9682 ± 0.0032 and r < 0.034 from the microwave background alone, and ns = 0.9728 ± 0.0029 once DESI is added, a shift the authors trace to a CMB-versus-DESI difference they cannot yet explain.  The article uses it for the current values of both inflation numbers and for which model shapes they favour.

    1. 21a.

      Section Abstract:  “Using data from Planck, the South Pole Telescope, Atacama Cosmology Telescope, and BICEP/Keck experiments, we derive ns = 0.9682 ± 0.0032 and a 95% upper limit of r < 0.034.  This upper limit on r is consistent with the official BICEP/Keck result given the numerical precision of the analyses … the r constraint is not impacted by the additional CMB data.” ↩ ↩

    2. 21b.

      Section Abstract:  “While adding DESI BAO data to the CMB data has a negligible impact on r, the ns constraint shifts upward to 0.9728 ± 0.0029, which favours monomial inflaton potentials with N⋆ ∼ 50 over Starobinsky R2 or Higgs inflation with N⋆ = 51 and N⋆ = 55, respectively.  This shift is caused by marginally significant differences between the CMB and DESI data that remain unexplained in the context of the standard model.  We show that a class of polynomial α-attractor models can predict the CMB as well as the CMB+DESI ns results.” ↩

    3. 21c.

      Section 3, Results, page 2:  “These constraints are consistent with the prediction of Starobinsky R2 and Higgs inflation at 2.0 σ and 1.3 σ, respectively.”  Page 4:  “the prediction of Starobinsky R2 inflation differs from the data at the 3.9 σ level.”  Page 4, footnote 9:  “We stress that this is for the theoretical predictions to lowest order in slow-roll parameters and for the chosen fiducial values of N⋆ … For both models, Starobinsky R2 and Higgs inflation, the predicted ns value can change depending on the details of reheating.”  Section 4, Conclusions, page 5:  “the addition of DESI data shifts the inferred ns value high, in favour of monomial inflaton potentials (with an exponent ∼ 1/3).” ↩

  22. 22.

    (1 − 0.9682) ÷ 0.0032 = 9.9.  This treats the error bar as Gaussian, the same way Planck does when it calls its own value of ns eight standard deviations from 1. ↩

  23. 23.

    Harrison, Edward R.  “Fluctuations at the threshold of classical cosmology.”  Physical Review D 1:2726–2730.  1970.  A 1970 paper by Edward R. Harrison on the scale-invariant spectrum, eleven years before inflation.  Scale-invariant means the fluctuations are about equally strong at every size.  The article uses it to show that scale invariance was not inflation's idea. ↩

  24. 24.

    Zel'dovich, Yakov B.  “A hypothesis, unifying the structure and the entropy of the universe.”  Monthly Notices of the Royal Astronomical Society 160:1P–3P.  1972.  A short paper of three pages in which Zel'dovich proposes a hypothesis linking the structure of the universe with its entropy.  The article uses it for the earlier prediction of ns = 1, which critics called trivial because it was made before inflation. ↩

  25. 25.

    Planck Collaboration.  “Planck 2018 results. IX. Constraints on primordial non-Gaussianity.”  Astronomy & Astrophysics 641:A9.  2020.  A Planck collaboration paper that tests the early fluctuations for primordial non-Gaussianity, a departure from a normal (Gaussian) pattern of fluctuations.  The article uses it for the measured value of the standard non-Gaussianity measure, fNL, which is consistent with zero.

    1. 25a.

      Section Abstract:  “Our combined temperature and polarization analysis produces the following final results:  fNLlocal = −0.9 ± 5.1;  fNLequil = −26 ± 47;  and fNLortho = −38 ± 24 (68 % CL, statistical).” ↩

  26. 26.

    Peiris, H. V. et al.  “First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation.”  Astrophysical Journal Supplement 148:213–231.  2003.  A paper on the first-year Wilkinson Microwave Anisotropy Probe (WMAP) observations, asking what they imply for inflation.  The article uses it because the paper says that the pre-Big-Bang and ekpyrotic scenarios also predict super-horizon fluctuations.

    1. 26a.

      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.” ↩ ↩

  27. 27.

    Ade, P. A. R. et al.  “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 paper by the BICEP/Keck Collaboration that combined all of its BICEP2, Keck Array and BICEP3 polarization data through the 2018 observing season with public WMAP and Planck maps.  It gives the strongest constraint to date on primordial gravitational waves, r < 0.036 at 95% confidence, and its simulations show an error of σ(r) = 0.009.  The article uses it as the best limit from B-mode data alone;  later combined analyses tighten it only slightly.

    1. 27a.

      Section Conclusions:  “The BKP analysis yielded a 95% confidence constraint r0.05 < 0.12, which BK14 improved to r0.05 < 0.09, and BK15 improved to r0.05 < 0.07.  The BK18 result described in this letter, r0.05 < 0.036, represents a fractional improvement equivalent to the two previous steps combined.” ↩

    2. 27b.

      Section Abstract:  “The likelihood analysis yields the constraint r0.05 < 0.036 at 95% confidence.  Running maximum likelihood search on simulations we obtain unbiased results and find that σ(r) = 0.009.” ↩

    3. 27c.

      “The φ2/3 model now lies outside the 95% contour as does the band of natural inflation models.” ↩ ↩

  28. 28.

    Tristram, M. et al.  “Improved limits on the tensor-to-scalar ratio using BICEP and Planck data.”  Physical Review D 105:083524.  2022.  A reanalysis that fitted r together with the six standard-model parameters, combining BICEP/Keck's 2018 B-mode data with Planck's reprocessed PR4 maps, baryon acoustic oscillations and microwave-background lensing.  The data are consistent with r = 0 and the combined 95% limit is r < 0.032, slightly tighter than BICEP/Keck alone.  The gain comes from combining existing data, not from new B-mode observations.  Mirror:  arXiv

    1. 28a.

      Section Abstract:  “the combination of Planck with BK18 and baryon-acoustic-oscillation data yields results consistent with r = 0 and tightens the constraint to r < 0.032 at 95% confidence.” ↩

  29. 29.

    CMB-S4 Project.  “Statement on the project's status.”  cmb-s4.org.  Jul 9, 2025.  Retrieved Aug 29, 2026.  The design goal is stated in CMB-S4 Science Case, Reference Design, and Project Plan, arXiv:1907.04473, as.  “σ(r) = 0.0005 for a non-detection.”  A public statement from the CMB-S4 project about its own status.  It reports that the U.S. Department of Energy and the National Science Foundation had stopped supporting the project, which then began an orderly shutdown.  The article uses it to show that one of the two experiments meant to settle the size of primordial gravitational waves no longer exists.

    1. 29a.

      “On July 9, 2025, the U.S. Department of Energy (DOE), Office of Science, Office of High Energy Physics and the U.S. National Science Foundation (NSF) issued a statement informing the CMB-S4 Project that 'DOE and NSF have jointly decided that they can no longer support the CMB-S4 Project.'  The CMB-S4 Project is proceeding with an orderly shutdown of the project.” ↩ ↩

  30. 30.

    LiteBIRD Collaboration (E. Allys et al.)  “Probing Cosmic Inflation with the LiteBIRD Cosmic Microwave Background Polarization Survey.”  Progress of Theoretical and Experimental Physics 2023(4):042F01.  2023.  A paper by the LiteBIRD collaboration on a survey of the polarization of the cosmic microwave background, the faint light left from the early universe, designed to probe cosmic inflation.  Its success criterion concerns r, the tensor-to-scalar ratio, which compares gravitational waves with density ripples.  The article uses it for the survey's stated success criterion, a total error below 0.001 on r.

    1. 30a.

      Section §3:  “The full success criterion of LiteBIRD is to achieve δr < 0.001 for a fiducial model with r = 0, where δr is the total error on the tensor-to-scalar ratio.” ↩ ↩

  31. 31.

    Ade, P. A. R. et al.  “Detection of B-Mode Polarization at Degree Angular Scales by BICEP2.”  Physical Review Letters 112:241101.  Jun 19, 2014.  A report by the BICEP2 Collaboration of a faint pattern of polarized light in the cosmic microwave background, which the team called a detection of B-mode polarization.  Its first version, posted on 17 March 2014, gave a tensor/scalar ratio of r = 0.20.  The article uses it as the claim that was reported worldwide as confirmation of inflation, and that its own authors later hedged in print.

    1. 31a.

      Abstract of v1 (17 March 2014).  “The observed B-mode power spectrum is well-fit by a lensed-LCDM + tensor theoretical model with tensor/scalar ratio r=0.20^{+0.07}_{-0.05}, with r=0 disfavored at 7.0σ.  Subtracting the best available estimate for foreground dust modifies the likelihood slightly so that r=0 is disfavored at 5.9σ.” ↩

    2. 31b.

      Abstract of the published version (v3, 23 June 2014), which replaced the dust sentence of the first version.  “We also examine a number of available models of polarized dust emission and find that at their default parameter values they predict power ∼(5−10)× smaller than the observed excess signal (with no significant cross-correlation with our maps).  However, these models are not sufficiently constrained by external public data to exclude the possibility of dust emission bright enough to explain the entire excess signal…  Accounting for the contribution of foreground dust will shift this value downward by an amount which will be better constrained with upcoming datasets.” ↩

    3. 31c.

      Endnote [95] of the published version:  “In the preprint version of this paper an additional DDM2 model was included based on information taken from Planck conference talks.  We noted the large uncertainties on this and the other dust models presented.  In the Planck dust polarization paper which has since appeared the maps have been masked to include only regions 'where the systematic uncertainties are small, and where the dust signal dominates total emission.'  This mask excludes our field.  We have concluded the information used for the DDM2 model has unquantifiable uncertainty.” ↩ ↩

  32. 32.

    Flauger, Raphael et al.  “Toward an Understanding of Foreground Emission in the BICEP2 Region.”  Journal of Cosmology and Astroparticle Physics 2014(08):039.  2014.  A reanalysis of the BICEP2 results, posted as arXiv:1405.7351 on 28 May 2014.  Its abstract says the data fit both a cosmology with r = 0.2 and negligible foregrounds, and a cosmology with r = 0 and a significant dust polarization signal, where r is the tensor-to-scalar ratio, which measures gravitational waves against density ripples.  The article uses it to show that independent groups found the ambiguity within ten weeks.

    1. 32a.

      Section Abstract:  “We reanalyze the Bicep2 results and show that the 100×150 GHz and 150×150 GHz data are consistent with a cosmology with r = 0.2 and negligible foregrounds, but also with a cosmology with r = 0 and a significant dust polarization signal.” ↩ ↩

  33. 33.

    Planck Collaboration.  “Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes.”  Astronomy & Astrophysics 586:A133.  2016.  A Planck collaboration paper on the polarized light from galactic dust at intermediate and high galactic latitudes, given as an angular power spectrum.  The arXiv preprint was submitted on 19 September 2014.  The article uses it because the dust signal in the BICEP2 field is about as large as the BICEP2 measurements, so dust alone could account for them.

    1. 33a.

      Section Conclusions:  On the BICEP2 field.  “Over the multipole range 40 < ℓ < 120, the Planck 353 GHz DℓBB power spectrum extrapolated to 150 GHz yields a value 1.32×10−2 µK2CMB…  This value is comparable in magnitude to the BICEP2 measurements at these multipoles that correspond to the recombination bump.” ↩

  34. 34.

    BICEP2/Keck and Planck Collaborations.  “A Joint Analysis of BICEP2/Keck Array and Planck Data.”  Physical Review Letters 114:101301.  2015.  A 2015 analysis that combined the BICEP2/Keck Array data with Planck data, submitted on 2 February 2015.  Its main finding is strong evidence for dust and no significant evidence for tensor modes, the pattern that primordial gravitational waves would leave.  The article uses it as the result that closed the BICEP2 dispute.

    1. 34a.

      Section Abstract:  “We find strong evidence for dust and no statistically significant evidence for tensor modes…  The final result is expressed as a likelihood curve for r, and yields an upper limit r0.05 < 0.12 at 95% confidence.” ↩ ↩

  35. 35.

    Kallosh, Renata et al.  “Superconformal Inflationary α-Attractors.”  Journal of High Energy Physics (11):198.  2013.  A theory paper that builds a family of inflation models inside supergravity, a framework that combines gravity with supersymmetry.  Its abstract says that for a small curvature parameter α the models converge on one shared prediction for the spectral index n_s and the tensor-to-scalar ratio r, and that the converged values fall where Planck measured them.  The article uses it to show that supergravity models can be built to match any possible pair of values for n_s and r.

    1. 35a.

      Section Abstract:  “for sufficiently large curvature (small α), the predictions converge to the universal attractor regime with ns = 1 − 2/N and r = α 12/N2, which corresponds to the part of the ns − r plane favored by the Planck data.” ↩

    2. 35b.

      Section §1, Introduction:  “we learned how to implement chaotic inflation with practically any desirable potential in supergravity with chiral matter multiplets as well as in supergravity with vector and tensor multiplets.  This allows to provide a consistent supergravity interpretation of any possible set of the observational parameters ns and r.” ↩

  36. 36.

    Planck Collaboration.  “Planck 2013 results. XXII. Constraints on inflation.”  Astronomy & Astrophysics 571:A22.  2014.  The collaboration's analysis of what its 2013 measurements of the cosmic microwave background mean for cosmic inflation.  It tests a number of inflation models against the data and finds a spectral index of 0.9603 ± 0.0073, which rules out exact scale invariance at over 5σ.  The article uses it for the models the data exclude, in the collaboration's own wording.

    1. 36a.

      Section Abstract:  “The Planck data thus shrink the space of allowed standard inflationary models, preferring potentials with V″ < 0.  Exponential potential models, the simplest hybrid inflationary models, and monomial potential models of degree n ≥ 2 do not provide a good fit to the data.” ↩ ↩

  37. 37.

    Ijjas, Anna et al.  “Inflationary paradigm in trouble after Planck2013.”  Physics Letters B 723:261–266.  2013.  A short letter by three authors that asks what the 2013 Planck satellite data mean for inflation.  Planck disfavors the simplest inflation models by 1.5 standard deviations or more, and the favored plateau-shaped models need an unusually smooth starting region and are unlikely under inflation's own reasoning.  The article uses it for the charge that these models need the very smoothness inflation was supposed to explain.

    1. 37a.

      Section end of §2:  “In sum, by favoring only plateau-like models, the Planck2013 data creates a serious new challenge for the inflationary paradigm:  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!” ↩

    2. 37b.

      Section §3:  “Obviously, 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.  The unlikeliness problem is an alarm warning us that a paradigm can fail even though observations favor a class of models if the paradigm predicts the class of models is unlikely.” ↩

    3. 37c.

      Section §2:  The plateau models require.  “initial smoothness on the scale of a billion or more Hubble volumes!” ↩

  38. 38.

    Ijjas, Anna et al.  “Pop Goes the Universe.”  Scientific American 316(2):32–39.  Feb 2017.  A general-audience essay by the three authors of the 2013 letter, one of whom, Steinhardt, was an original architect of inflationary theory and later pointed out serious problems with its foundations.  It argues that the Planck data and inflation's theoretical problems have shaken the theory, and that inflation can be made to predict almost any outcome.  The article quotes it for two charges: that starting inflation needs the same smoothness inflation was meant to explain, and that inflation cannot be tested.

    1. 38a.

      Page 38:  “More important, 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.  Recall that the entire motivation for introducing it was to explain how the visible universe came to have these properties; if starting inflation requires those same properties, with the only difference being that a smaller patch of space is needed, that is hardly progress.” ↩

    2. 38b.

      Page 39:  “inflationary cosmology, as we currently understand it, cannot be evaluated using the scientific method.  As we have discussed, the expected outcome of inflation can easily change if we vary the initial conditions, change the shape of the inflationary energy density curve, or simply note that it leads to eternal inflation and a multimess.  Individually and collectively, these features make inflation so flexible that no experiment can ever disprove it.” ↩

  39. 39.

    Guth, Alan H.  “Eternal Inflation and Its Implications.”  Journal of Physics A 40:6811–6826.  2007.  A talk by Alan H. Guth, given at the 2006 IRGAC conference in Barcelona, posted as arXiv:hep-th/0702178 and printed in the Journal of Physics A.  Eternal inflation means that inflation, once started, keeps going forever in some regions and creates pocket universes; the talk argues that the evidence for inflation is strong and reviews the ambiguities in calculating probabilities in eternally inflating spacetimes.  The article uses it for Guth's statement that inflation is eternal into the future but not into the past, and for his credit of the discovery of eternal inflation to Steinhardt.

    1. 39a.

      Section 4, Difficulties in Calculating Probabilities:  “In an eternally inflating universe, anything that can happen will happen; in fact, it will happen an infinite number of times.  Thus, the question of what is possible becomes trivial—anything is possible, unless it violates some absolute conservation law.  To extract predictions from the theory, we must therefore learn to distinguish the probable from the improbable.” ↩

    2. 39b.

      Section Abstract:  “Although inflation is generically eternal into the future, it is not eternal into the past.” ↩

    3. 39c.

      Section 2.1, Eternal New Inflation:  “The eternal nature of new inflation was first discovered by Steinhardt [24], and later that year Vilenkin [25] showed that new inflationary models are generically eternal.” ↩ ↩

  40. 40.

    Steinhardt, Paul J.  “Big Bang blunder bursts the multiverse bubble.”  Nature 510:9.  Jun 3, 2014.  A "World View" opinion column in Nature by Paul Steinhardt, professor of physics at Princeton University, written after a claimed detection of primordial gravitational waves was undercut by a reanalysis that found the signal could come from foreground effects.  It argues that inflation is so flexible that no test could rule it out.  The article quotes its sharpest sentence, which uses the word "untestable."

    1. 40a.

      “Taking this into account, it is clear that the inflationary paradigm is fundamentally untestable, and hence scientifically meaningless.” ↩

  41. 41.

    Guth, Alan H. et al.  “Inflationary Paradigm after Planck 2013.”  Physics Letters B 733:112–119.  2014.  A 2014 journal paper by Alan H. Guth, David I. Kaiser and Yasunori Nomura on the inflationary paradigm after the 2013 Planck results, posted as arXiv:1312.7619.  The article uses it as the authors' reply to the 2013 version of the critics' argument, and for their admission that no one has yet found a persuasive theory of probabilities in the multiverse.

    1. 41a.

      Section IV, The Multiverse and Predictivity:  “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.” ↩

    2. 41b.

      Section Concluding section:  “although significant progress has been made in recent years, a persuasive theory of probabilities in the multiverse has not yet been found.” ↩ ↩

    3. 41c.

      Section IV:  “To us, the measure problem is simply an important problem that remains to be solved.”  “While Johnson and Lehners confined their remarks to a subclass of cyclic models, we believe that the measure problem exists in all cyclic models.” ↩

  42. 42.

    Penrose, Roger.  The Road to Reality: A Complete Guide to the Laws of the Universe.  Jonathan Cape.  2004.  A book by Roger Penrose that is a complete guide to the laws of the universe.  Its critique of inflation is in section 28.5, pages 753–757.  The article uses it because Penrose states his doubts about inflation with care about their scope.

    1. 42a.

      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.” ↩

    2. 42b.

      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.” ↩

  43. 43.

    Albrecht, Andreas.  “Cosmic Inflation and the Arrow of Time.”  arXiv.  2002.  An essay by a UC Davis physicist, Andreas Albrecht, who co-authored one of the two 1982 new-inflation papers.  It asks whether inflation can explain the one-way arrow of time, the reason a dropped glass breaks but never reassembles, and it compares inflation with rival theories of the universe's starting conditions.  The article uses it because its author concedes the point in print.

    1. 43a.

      Section 5.2 Inflation and the arrow of time:  “inflation does not predict the arrow of time.  Inflation 'passes the arrow of time buck' to the special initial conditions of the inflaton field.” ↩

  44. 44.

    Ross, Hugh.  “Cosmic Inflation: It Really Happened.”  Reasons to Believe.  Aug 3, 2015.  A web article by Hugh Ross, published on the Reasons to Believe website.  It argues from the spectral index, ns, that inflation is certain to 99.9999999 percent, and that the Bible anticipated big bang cosmology.  The article quotes its certainty figure and its claim about the Bible, and answers both.

    1. 44a.

      “The SPT team proved the reality of cosmic inflation to 6.075 standard deviations—(1.0 – 0.9593)/0.0067.  That number of standard deviations translates into a certainty measure for the reality of cosmic inflation.  In light of the team's measurements, we now can be 99.9999999 percent certain that the universe indeed went through an inflation event when the universe was only about 10-34 seconds old.” ↩

    2. 44b.

      “For a universe with no inflation event, ns equals 1.0 or greater.  For a universe that had a simple inflation event, ns equals exactly 0.95.  For a universe that has had a complex inflation event, ns equals 0.96–0.97.” ↩

    3. 44c.

      “This is good news for Christians because for more than 2,500 years the Bible and biblical commentaries were the only books proclaiming the fundamental features of big bang cosmology”.  The list has four features.  The second cites Job 9:8; Psalm 104:2; Isaiah 40:22 and eight more.  “A singular beginning of matter, energy, space, and time”.  “Ongoing expansion since that beginning”.  “Constant laws of physics”.  “A pervasive law of decay”. ↩

  45. 45.

    Hartnett, John G.  “Cosmic Inflation: Did it really happen?”  creation.com.  Creation Ministries International.  Sep 1, 2015.  A 2015 web article by John G. Hartnett asking whether cosmic inflation really happened; it was updated on 11 September 2015.  The article uses it for Hartnett's argument that the claim of proof for inflation rests on the model rather than the data, since a similar spectral-index value in 2013 was not claimed as proof of inflation.

    1. 45a.

      “Now the claim of proof that the inflation event really happened hinges on the value of ns.  But what requires that that number must be less than unity to 'prove' inflation really occurred?  The modelling does.” ↩

    2. 45b.

      “When the Planck satellite polarization data was published in 2013, a very similar number was produced (ns = 0.9603 ± 0.0073 when combined with WMAP polarization data) but no claim of proof of inflation was made then.” ↩

    3. 45c.

      On Isaiah 40:22:  “These are similes, and as such should carry some correspondence over to the intended meaning.  But I have never heard of a tent being stretched by anything like that.” ↩

  46. 46.

    Disney, Michael J.  “Modern Cosmology: Science or Folktale?”  American Scientist 95(5):383–385.  2007.  The author opens by apologising for.  “such a highly opinionated attack.”  An essay in American Scientist by a Cardiff astronomer who is not a creationist.  It argues that big bang cosmology is five separate theories built on top of one another.  The article uses it as a secular astronomer's list of those five layers, with inflation the second.

    1. 46a.

      “Big Bang cosmology is not a single theory; rather, it is five separate theories constructed on top of one another.  The ground floor is a theory, historically but not fundamentally rooted in general relativity, to explain the redshifts—this is Expansion…  The second floor is Inflation—needed to solve the horizon and 'flatness' problems of the Big Bang.  The third floor is the Dark Matter hypothesis…  The fourth floor is some kind of description for the 'seeds' from which such structure is to grow.  And the fifth and topmost floor is the mysterious Dark Energy…  Thus Dark Energy could crumble, leaving the rest of the building intact.  But if the Expansion floor collapsed, the entire edifice above it would come crashing down.” ↩

  47. 47.

    Hartnett, John G.  “Big bang beliefs: busted.”  Creation 37(3):48–51.  Jul 2015.  A young-earth magazine article in Creation that lists what it calls the big bang's unsolved problems, including faster-than-light inflation.  The web edition appeared on 14 April 2016 and was updated on 6 March 2017.  The article uses it as a typical young-earth charge against inflation, and it concedes one fair point from it.

    1. 47a.

      Section Standfirst:  “Big bang cosmogony requires many fudge factors to stay afloat, including dark matter, dark energy, and faster-than-light inflation.”  The article's table of "unknowns" lists the following.  “Flatness (space has Euclidean geometry) and isotropy (uniformity in all directions), explained by faster-than-light inflation.” ↩

    2. 47b.

      “This is a cosmological fine-tuning problem, where the force of the expansion matched the force of gravity to one part in 1060.  Furthermore, since the universe has departed from the needed critical density over cosmic time, it must have been even closer to perfect flatness soon after the big bang.” ↩

    3. 47c.

      “However, there is no good mechanism to cause this faster-than-light expansion, or to stop it once it began.” ↩

  48. 48.

    Borde, Arvind et al.  “Inflationary Spacetimes Are Incomplete in Past Directions.”  Physical Review Letters 90:151301.  2003.  A 2003 paper by Arvind Borde, Alan Guth and Alexander Vilenkin, whose title says that inflating spacetimes are incomplete in past directions, meaning their history cannot be traced back forever.  The article uses it as the proof that inflation alone does not remove the need for a beginning.  Mirror:  arXiv

    1. 48a.

      Section Concluding section:  “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.” ↩

  49. 49.

    Guth, Alan H.  “Inflation.”  Carnegie Observatories Astrophysics Series 2.  2004.  A review chapter by Alan H. Guth of MIT, from the Carnegie Observatories volume Measuring and Modeling the Universe, posted as arXiv:astro-ph/0404546.  Its abstract says that under reasonable assumptions the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe its past boundary.  The article uses it because Guth himself denies that this theorem establishes a unique beginning.

    1. 49a.

      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.” ↩

  50. 50.

    Vilenkin, Alexander.  “The Beginning of the Universe.”  Inference: International Review of Science 1(4).  Oct 2015.  A critical essay by Alexander Vilenkin, one of the authors of the Borde-Guth-Vilenkin theorem.  The theorem says that if the universe is on average expanding, its history cannot be continued indefinitely into the past.  The article uses the essay for Vilenkin's own answer to the question of a beginning, and for his statement that the theorem says nothing about God.

    1. 50a.

      Section An Unaddressable Mystery:  The final section of the essay.  “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.”  “When physicists or theologians ask me about the BGV theorem, I am happy to oblige.  But my own view is that the theorem does not tell us anything about the existence of God.” ↩

  51. 51.

    Khoury, Justin et al.  “The Ekpyrotic Universe: Colliding Branes and the Origin of the Hot Big Bang.”  Physical Review D 64:123522.  2001.  A theory paper that proposes an alternative to inflation: the universe starts cold and empty, and a brane (a membrane in extra dimensions) collides with a plane to produce the hot big bang.  The paper says its model addresses the horizon, flatness and monopole problems and gives a nearly scale-invariant spectrum of density perturbations, without invoking inflation.  The article uses it as a live rival to inflation, to argue that the horizon problem is a puzzle rather than a crisis.

    1. 51a.

      Section Abstract:  “We propose a cosmological scenario in which the hot big bang universe is produced by the collision of a brane in the bulk space with a bounding orbifold plane, beginning from an otherwise cold, vacuous, static universe.  The model addresses the cosmological horizon, flatness and monopole problems and generates a nearly scale-invariant spectrum of density perturbations.” ↩

  52. 52.

    Feeney, Stephen M. et al.  “First Observational Tests of Eternal Inflation.”  Physical Review Letters 107:071301.  2011.  A 2011 paper that searched the WMAP microwave background data for the marks that collisions with other bubble universes would leave, the first observational test of eternal inflation.  The article uses it because it is the test that has already been run, and it came back null.  Mirror:  arXiv

    1. 52a.

      Section Abstract:  “We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite.  We conclude that the WMAP 7-year data do not warrant augmenting ΛCDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky N̄s < 1.6 at 68% CL.” ↩