Rival Cosmologies

Faulkner, Danny R.  “The Case for Cosmological Redshifts.”  Answers Research Journal 11:31–47.  2018.  A 2018 journal article by Danny R. Faulkner arguing that the redshifts of galaxies and quasars are cosmological, that is, caused by the expansion of the universe.  The article cites it for three points:  that Halton Arp accepted an expanding universe, that his probability argument asked the question the wrong way round, and that the directors of the Palomar and NOAO observatories cut off his telescope time.

1. 1a.

   Page 46:  “Rejection of universal expansion seems to be motivated by opposition to the big bang model.  If the universe is not expanding, then the big bang model is not viable.  However, the big bang is just one possible expanding universe cosmology.  This short-cut way of undermining the big bang model could be a huge mistake, for if the universe is expanding, but we reject this, it would be impossible to construct a correct biblical cosmology.”  Section Abstract:  The abstract's own summary is milder:  “Rejection of cosmological redshifts could stifle development of a true biblical cosmology.” ↩ ↩

2. 1b.

   Page 46:  Faulkner says that rejecting cosmological redshifts.  “amounts to a rejection of general relativity, one of the most successfully tested theories in the history of science.  If the universe is expanding, then it follows that the redshifts of extragalactic objects, including quasars, are cosmological.” ↩ ↩

3. 1c.

   Page 44:  “Furthermore, contrary to common misconception among recent creationists, Arp and other astronomers who questioned whether quasars had cosmological redshifts never doubted that the universe was expanding.  Indeed, Arp and his colleagues clung to the steady state model long after nearly everyone else had abandoned it.  The steady state model is not possible if the universe is not expanding, so it would have made no sense for Arp and his colleagues to have doubted universal expansion.” ↩

4. 1d.

   Page 37:  “This led to the directors of the Palomar Observatory and National Optical Astronomy Observatory collectively informing Arp that he no longer would be granted telescope time at either institution to pursue this work.  Arp was free to pursue other types of research, but not the type of work he had dedicated his life to.” ↩ ↩

5. 1e.

   Page 37:  “Consequently, some recent creationists express doubts about reality of the Hubble relation and cosmological redshifts while simultaneously embracing the galactocentric implications of quantized redshifts without realizing the inherent contradiction of these two positions.” ↩

Wieland, Carl.  “Secular scientists blast the big bang: What now for naïve apologetics?”  Creation 27(2):23–25.  Mar 2005.  A 2005 article in Creation magazine by Carl Wieland of Creation Ministries International, a creationist ministry, and posted on its website on 2 February 2006.  It answers a 2004 open letter from 33 scientists who doubted the big bang.  The article uses it as the creationist reply to that letter, which it says is still in circulation.

1. 2a.

   “Those who developed the big bang were guided by secular worldview filters just as much as those who are now crying that the emperor has no clothes.  They wanted a universe that created itself; their opponents want an eternal, uncreated universe.  From a Christian perspective, both are in open defiance of their Creator's account of what really happened.”  Wieland writes "33 leading scientists" and "the 33 dissidents"; the list carries 34 names. ↩ ↩

Blondin, S. et al.  “Time Dilation in Type Ia Supernova Spectra at High Redshift.”  Astrophysical Journal 682:724–736.  2008.  A paper by 32 authors that measured how fast 13 high-redshift Type Ia supernovae appear to age, using 35 spectra.  Its abstract says the results confirm the expansion hypothesis and unambiguously exclude models that predict no time dilation, such as Zwicky's tired light hypothesis.  The article uses its Table 4 numbers for the full sample to show how badly tired light fits the data.  Mirror:  arXiv

1. 3a.

   Section §5 (Conclusion), table 4:  The sample is.  “35 spectra of 13 high-redshift (0.28 ≤ z ≤ 0.62) SNe Ia.”  Fitting an aging rate of 1/(1 + z)^b gives.  “b = 0.97 ± 0.10 for the entire sample”.  “b = 0.95 ± 0.10 for the high-redshift sample.”  Table 4 gives, for all supernovae: the 1/(1 + z) model has χ²/dof = 27.0/35 and goodness of fit 83.2 percent, and the tired light model has χ²/dof = 150.3/35 and goodness of fit 0.0 percent.  Section §4:  “the hypothesis of no time dilation is not a good fit to the data (χ² = 150.3 for 35 degrees of freedom).” ↩ ↩ ↩

Lubin, Lori M., and Allan Sandage.  “The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies.”  Astronomical Journal 122(3):1084–1103.  2001.  Paper IV of the Tolman surface-brightness series.  It measures the test on Hubble Space Telescope images of 34 early-type galaxies in three clusters at redshifts 0.76, 0.90 and 0.92, and it also tests tired light with the same data.  The authors conclude that the test is consistent with the reality of the expansion once the brightening of ageing stars (luminosity evolution) is allowed for.  The article uses the paper for its measured exponent and for its 10 σ test of tired light.  Mirror:  arXiv

1. 4a.

   Section Abstract:  “We have also used the high-redshift HST data to test the 'tired light' speculation for a non-expansion model for the redshift.  The HST data rule out the 'tired light' model at a significance level of better than 10 σ.” ↩ ↩ ↩

2. 4b.

   Section Abstract:  “Expressed as the exponent, n, in 2.5 log (1 + z)ⁿ mag, the value of n for all three clusters is n = 2.59 ± 0.17 in the R band and 3.37 ± 0.13 in the I band for a q_o = 1/2 model.” ↩

3. 4c.

   Section Abstract:  “For a true Tolman signal with n = 4, the luminosity evolution in the look-back time… must then be between 1.72 to 1.19 in the R band and 0.94 to 0.45 in the I band.  We show that this is precisely the range expected from the evolutionary models of Bruzual & Charlot.” ↩

Fixsen, D. J. et al.  “The Cosmic Microwave Background Spectrum from the Full COBE FIRAS Data Set.”  Astrophysical Journal 473:576–587.  1996.  A reanalysis of the low-frequency data from the FIRAS instrument on NASA's COBE satellite, taken over its ten-month mission, except for the first month.  FIRAS compares the sky with a precise blackbody spectrum, and the paper gives new, tighter limits on any departure from one.  The article uses its result as a decisive test of the background's spectrum.  Mirror:  arXiv

1. 5a.

   Section Abstract:  “The FIRAS measures the difference between the cosmic microwave background and a precise blackbody spectrum.  We find new tighter upper limits on general deviations from a blackbody spectrum.  The RMS deviations are less than 50 parts per million of the peak of the CMBR.  For the Comptonization and chemical potential we find |y| < 15 × 10⁻⁶ and |µ| < 9 × 10⁻⁵ (95% CL).  There are also refinements in the absolute temperature, 2.728 ± 0.004 K (95% CL).” ↩ ↩ ↩

Lisle, Jason.  “Sizes of Galaxies in JWST Data Suggest New Cosmology.”  Answers Research Journal 17:445–457.  2024.  A paper by the young-earth creationist Jason Lisle in a journal of Answers in Genesis.  It takes the apparent sizes of galaxies in JWST deep-field images and tests them against a model in which galaxies recede through space that does not expand, so that redshift is a Doppler shift.  It reports that the data fit that model and fail the standard expanding-universe model, and the article uses it as the creationist case that the new JWST data favour the Doppler model; the three-paper exchange starts here.

1. 6a.

   Page 454:  “The average of these two exponents is 2.98 ± 0.55, consistent with the Doppler model prediction of 3, but well below the standard model's prediction of 4.” ↩

2. 6b.

   Page 449:  Equation (11):  “L_R = [(1 − v/c)/(1 + v/c)]³”.  and equation (12):  “L_R = 1/(z + 1)³”.  For a relativistic Doppler shift, (1 − v/c)/(1 + v/c) = (1 + z)⁻² exactly, so the cube of equation (11) is (1 + z)⁻⁶, not (1 + z)⁻³.  Equation (13), the luminosity distance D_D(1 + z)^1.5, follows from equation (12). ↩

3. 6c.

   Page 454:  “The Doppler model therefore passes the Tolman test while the standard ΛCDM model and the tired light model do not.” ↩

Holanda, R. F. L. et al.  “Testing the Distance-Duality Relation with Galaxy Clusters and Type Ia Supernovae.”  Astrophysical Journal Letters 722:L233–L237.  2010.  A letter that tests the distance-duality relation, the rule linking two ways of measuring distance, with Type Ia supernovae matched to galaxy clusters.  For the spherical-cluster sample it finds a departure of η₀ = −0.42 at 3σ, which the authors call clearly incompatible with the relation.  The article uses the paper for its statement that the relation holds for every cosmology built on Riemannian geometry, whatever the matter in it.  Mirror:  arXiv

1. 7a.

   Section §1:  Stated immediately after the equation D_L(1 + z)⁻²/D_A = 1.  “This equation is completely general, valid for all cosmological models based on Riemannian geometry, being dependent neither on Einstein field equations nor the nature of matter-energy content.  It only requires that source and observer are connected by null geodesics in a Riemannian spacetime and that the number of photons are conserved.  Therefore, it is valid for spatially homogeneous and isotropic (anisotropic) cosmologies, as well as for inhomogeneous cosmological models.”  Other articles have credited this sentence to Renzi, Hogg and Giarè 2022, but it is not in that paper.  It is Holanda, Lima and Ribeiro's, and it should be cited to them. ↩ ↩ ↩

Lisle, Jason.  “Sizes of Galaxies in JWST Data and Cosmology — Reply to Barnes.”  Answers Research Journal 18:441–447.  2025.  Lisle's answer to Barnes's reply, in the same journal.  He says he reproduced Barnes's SAGE result with the same simulation and parameters, and that the model Barnes defended was already disproved years ago by galaxy mass and luminosity data from JWST deep fields.  The article uses it for Lisle's claim that the Doppler model is currently the only model that passes the Tolman test, which checks how fast the surface brightness of distant galaxies fades with distance, and for his concession that the Doppler model is not needed to explain distant starlight.

1. 8a.

   Page 446:  “Quite right.  The Doppler model is not needed to explain distant starlight in a young universe.  Rather, it was invoked to explain the angular size and luminosity data in JWST deep fields.” ↩

2. 8b.

   Page 447:  “And since the ASC model doesn't assume any particular metric, it is compatible with either the FLRW metric or the Doppler model.” ↩

3. 8c.

   Page 442:  “Of course, the actual metric of the universe cannot be Minkowski because this metric applies to space with negligible mass.  But it is an example of a non-expanding metric in contrast to the FLRW metric.” ↩ ↩

4. 8d.

   Page 446:  “Barnes is correct when he states, “Lisle proposes to solve this [the distant starlight problem] with the Anisotropic synchrony convention, which implies that we see galaxies as they are now, regardless of how far away they are.  This gives the model enough freedom that any observed population of galaxies is consistent with a young universe” (Barnes 2024).  Quite right.” ↩

5. 8e.

   Page 447:  “Very few advocates of the big bang are willing to read and interact with creation technical literature.  And so, I sincerely wish to thank Luke Barnes for his interest and his constructive criticism.” ↩

Bahcall, John N. et al.  “The Near-Ultraviolet Spectrum of Markarian 205.”  The Astrophysical Journal 398(2):495–500.  Oct 20, 1992.  A near-ultraviolet spectrum of the quasar Markarian 205, taken with the Hubble Space Telescope at a resolution of R = 1300.  It found 15 absorption lines, the dark lines where gas has taken light out of the spectrum, and two of them, a pair of magnesium lines called the Mg II doublet, come from gas in the galaxy NGC 4319.  The article uses it as the test of Arp's flagship case, because gas in the galaxy absorbing the quasar's light shows that the light passes through the galaxy.

1. 9a.

   Section §6, page 498:  “Our best estimate for the heliocentric velocity of the Mg II absorption feature associated with NGC 4319 is”.  The displayed equation (2a) gives this as ⟨cz_⟩I_⟩heliocentric~ = 1265 ± 55 km s⁻¹.  The paper gives NGC 4319's own heliocentric velocity as "about 1405 km s⁻¹ or z = 0.00468" (§1, p. 495), citing Bowen et al. 1991 and Sulentic & Arp 1987a. ↩ ↩

Hawkins, E. et al.  “No Periodicities in 2dF Redshift Survey Data.”  Monthly Notices of the Royal Astronomical Society 336:L13.  2002.  A 2002 test of a claimed repeating pattern in quasar redshifts (quasars are very bright, distant objects), run on 1,647 quasar-galaxy pairs from the 2dF galaxy and quasar surveys, almost eight times the sample of the earlier positive result.  William Napier, who had briefed the authors on the claim, set the test and took no part in the analysis, and it found no periodicity at the predicted frequency.  The article uses it as one of the two failed tests of the periodicity prediction.  Mirror:  arXiv

1. 10a.

   Section Abstract:  “These data provide by far the largest and most homogeneous sample for such a study, yielding 1647 QSO-galaxy pairs.  There is no evidence for a periodicity at the predicted frequency in log(1 + z), or at any other frequency.” ↩ ↩

2. 10b.

   Section Acknowledgements:  “We are most grateful to Bill Napier for suggesting that we undertake this study, and for setting up such a fair test of this hypothesis.” ↩

Wright, Edward L.  Comments on the Quasi-Steady-State Cosmology.  Oct 20, 1994.  A UCLA preprint (UCLA-ASTRO-ELW-94-04) by Edward L. Wright, never published in a journal, which tests the quasi-steady-state cosmology of Hoyle, Burbidge and Narlikar against the cosmic microwave background and against radio source counts.  Wright had been the referee who recommended against one of the QSSC papers, which Hoyle, Burbidge and Narlikar say in their reply; Wright himself writes that the failure "was fully explained to both HBN and to the editor of MNRAS in a referee's report dated July 1993… but HBN proceeded to publish incorrect results."  He was a COBE co-investigator and a co-author of the FIRAS spectrum paper, and the article uses the preprint to show that the model predicts blueshifts among bright radio sources that are not observed.

1. 11a.

   Section §4, Blueshifts, page 6:  “Note that the blueshifted fraction jumps to more than 90% for the brightest sources that show a steeper than Euclidean source count.  Thus the 3CR sample, which has source counts that are significantly steeper than Euclidean, should be dominated by blueshifts if the QSSC were correct.  While it is possible to have no blueshifts in the 3CR flux range by a suitable choice of the luminosity function, one then predicts source counts that are substantially less steep than Euclidean, producing a > 3σ discrepancy in source count slopes between the model and the data.  At the peak of N F^1.5, the blueshifted fraction predicted by the QSSC is > 75%.  The 1 Jy sample of Allington-Smith et al. (1988) is at the peak of N F^1.5, has a secure redshift completeness > 80% … and no blueshifts.  Since one can not fit a > 75% blueshifted fraction into a < 20% unidentified fraction, the QSSC prediction is false.” ↩ ↩

Cohen, A. G. et al.  “A Matter-Antimatter Universe?”  ApJ 495:539–549.  1998.  A theory paper asking whether the universe could be a patchwork of regions of matter and regions of antimatter, and estimating the gamma rays given off where the two meet.  It finds that such a patchwork would produce a gamma-ray signal above the observational limits unless the matter region is virtually the entire visible universe.  Its authors state their own limit: small, distant pockets of antimatter cannot be ruled out.  The article uses it to show that Alfvén's cosmology, which needed equal parts matter and antimatter, would produce gamma rays that are not observed.  Mirror:  arXiv

1. 12a.

   Section 7 Conclusions, pages 19–20:  Page numbers of the arXiv preprint.  “Direct searches for annihilation radiation show that d₀ > 20 Mpc… Our conservative estimate of the relic CDG flux far exceeds its measured value.  Thus, we have ruled out a B = 0 universe with domains smaller than a size comparable to that of the visible universe.” ↩ ↩

Milgrom, Mordehai.  “A Modification of the Newtonian Dynamics: Implications for Galaxies.”  ApJ 270:371–383.  1983.  The second of Milgrom's three 1983 papers on modified Newtonian dynamics (MOND).  Its abstract lists the predictions the theory makes for galaxy rotation curves and gives its acceleration constant, a₀.  The article quotes those predictions as the tests the theory set for itself.

1. 13a.

   Section Abstract, page 371:  “The main predictions are:  1.  Rotation curves calculated on the basis of the observed mass distribution and the modified dynamics should agree with the observed velocity curves.  2.  The V_∞⁴ = a₀GM relation should hold exactly.  3.  An analog of the Oort discrepancy should exist in all galaxies and become more severe with increasing r in a predictable way.”  Result 5 of the same abstract:  “The value of the acceleration constant, a₀, determined in a few independent ways is approximately 2 × 10⁻⁸ (H₀/50 km s⁻¹ Mpc⁻¹)² cm s⁻², which is of the order of cH₀ = 5 × 10⁻⁸ (H₀/50 km s⁻¹ Mpc⁻¹) cm s⁻².” ↩ ↩

Skordis, Constantinos, and Tom Złośnik.  “New Relativistic Theory for Modified Newtonian Dynamics.”  Physical Review Letters 127:161302.  2021.  A 2021 paper that proposes a relativistic gravity theory giving modified Newtonian dynamics (MOND) in galaxies, called aether scalar tensor theory (AeST).  Its abstract says it agrees with the cosmic microwave background and matter power spectra on large scales, and that its action is free of ghost instabilities at second order.  The article calls it the current best attempt.  Mirror:  arXiv

1. 14a.

   Section Cosmology, page 4:  Preprint page.  “For a wide range of parameters, this relativistic MOND theory is consistent with the CMB measurements from Planck.  This happens because c²_ad and w are small enough so that Π → 0 and we get dustlike evolution.” ↩ ↩

Noterdaeme, P. et al.  “The Evolution of the Cosmic Microwave Background Temperature: Measurements of T_CMB at High Redshift from Carbon Monoxide Excitation.”  Astronomy & Astrophysics 526:L7.  2011.  A measurement of the background temperature at high redshift, made from carbon monoxide.  The article uses its result as a test of how the background temperature changes with redshift.  Mirror:  arXiv

1. 15a.

   Section Abstract:  “Combining our precise measurements with previous constraints, we obtain T_CMB(z) = (2.725 ± 0.002) × (1+z)^(1−β) K with beta = −0.007 ± 0.027, a more than two-fold improvement in precision.”  Sunyaev-Zel'dovich determinations give a joint deviation parameter α = −0.001 ± 0.012 (Hurier et al., A&A 561:A143, 2014;  de Martino et al., ApJ 808:128, 2015). ↩ ↩ ↩ ↩

Hoyle, F.  “A New Model for the Expanding Universe.”  Monthly Notices of the Royal Astronomical Society 108:372–382.  1948.  A 1948 paper by Hoyle, received on 5 August 1948, that sets out the steady-state idea.  It shows that continuous creation of matter lets a universe expand while its density stays constant, with no need for Einstein's cosmological constant (a term in Einstein's equations).  The article uses it for Hoyle's own reason for the idea: the aesthetic objection to creation in the remote past.

1. 16a.

   Page 372:  “This possibility seemed attractive, especially when taken in conjunction with aesthetic objections to the creation of the universe in the remote past.  For it is against the spirit of scientific enquiry to regard observable effects as arising from 'causes unknown to science', and this in principle is what creation-in-the-past implies.” ↩ ↩ ↩

Hartnett, John G.  “Unknown Selection Effect Simulates Redshift Periodicity in Quasar Number Counts from Sloan Digital Sky Survey.”  Astrophysics and Space Science 324:13–16.  2009.  A short paper by a physicist who had championed quantized redshifts, on quasar counts in Sloan Digital Sky Survey data, which finds that an apparent periodicity is a selection effect.  The article cites it as the decisive paper, and its author is a creationist.  Mirror:  arXiv

1. 17a.

   Section Abstract:  “However the same periods are found in the mean of the zConf parameter used to flag the reliability of the spectroscopic measurements.  It follows that these redshift periods must result from some selection effect, as yet undetermined.  It does not signal any intrinsic (quantized) redshifts in the quasars.” ↩

Zwicky, F.  “On the Red Shift of Spectral Lines through Interstellar Space.”  Proceedings of the National Academy of Sciences 15(10):773–779.  1929.  A short theory paper that proposes a new effect of masses on light, described as a sort of gravitational analogue of the Compton effect, to explain the apparent velocity of recession of distant nebulae.  It was communicated to the journal on 26 August 1929, and it is the original tired-light proposal that the article examines.

1. 18a.

   Page 775, section §F, The Gravitational 'Drag' of Light:  “According to the relativity theory, a light quantum hν has an inertial and a gravitational mass hν/c².  It should be expected, therefore, that a quantum hν passing a mass M will not only be deflected but it will also transfer momentum and energy to the mass M and make it recoil.  During this process, the light quantum will change its energy and, therefore, its frequency.” ↩

2. 18b.

   Page 775, section §D:  “Also, it is evident that any explanation based on a scattering process like the Compton effect or the Raman effect, etc., will be in a hopeless position regarding the good definition of the images as mentioned under B₄.” ↩

3. 18c.

   Page 778:  The result is.  “Δν/ν = 1.4π f ρ D L / c².”  The inputs:  “For the total space investigated, the possible limits for ρ are according to E. Hubble 10⁻²⁶ gr./cm.³ > ρ > 10⁻³¹.  The mutual distance l of the galactic systems being of the order l = 10⁶ parsecs, we may assume D for instance of the order 1000 l = 3 × 10²⁷ cm.”  The output:  “Then Δν/ν for L = 10⁶ parsecs according to our formula will be in the limits 3 × 10⁻² > Δν/ν > 3 × 10⁻⁷.  From Hubble's linear relation, we have Δν/ν ∼ 1/600 for the same L.  In view of this agreement in order of magnitude, a further elaboration of the theory seems to be worthwhile.” ↩

Scolnic, Dan et al.  “The Pantheon+ Analysis: The Full Data Set and Light-Curve Release.”  The Astrophysical Journal 938:113.  2022.  The full data set and light-curve release for Pantheon+, a large collection of Type Ia supernovae.  The article's fits use 1,371 of them, those above z = 0.023, with diagonal (uncorrelated) statistical errors and the absolute-magnitude offset marginalised analytically, meaning averaged out mathematically.  The article uses it as the test Lisle proposed for Type Ia supernovae, since its distances and redshifts are a public download. ↩

The supernova fits are the Doppler article's own, on the public Pantheon+ distances.  It used the 1,371 supernovae above z = 0.023 that are not distance-ladder calibrators, marginalised the absolute magnitude and Hubble constant so that only the shape of the distance-redshift curve is tested, and used diagonal statistical errors only.  Against a standard model with Ω_M = 0.3 it reports Δχ² of 29 for the coasting Milne model, 126 for Lisle's model as published, 1,785 for Lisle's model with reciprocity enforced and 1,583 for tired light, with the same order when the lowest redshifts are cut at z > 0.1 or z > 0.2.  The script is pantheon_fit.py. ↩

Sayers, Jack et al.  “A Measurement of the Kinetic Sunyaev-Zel'dovich Signal Toward MACS J0717.5+3745.”  The Astrophysical Journal 778(1):52.  2013.  A measurement of the kinetic Sunyaev-Zel'dovich effect, the Doppler-type shift that hot gas in a moving galaxy cluster gives the microwave background, toward the cluster MACS J0717.5+3745.  The best-fit line-of-sight velocity for sub-cluster B is +3,450 ± 900 km/s, and the article uses it as a direct measure of the speed of a fast-moving merging cluster.  Mirror:  arXiv ↩ ↩

Arp, Halton.  “A Connection Between the Spiral Galaxy NGC 4319 and the Quasi-Stellar Object Markarian 205.”  Astrophysical Letters 9:1–4.  1971.  A four-page letter in which Arp reports a luminous filament joining the quasar Markarian 205 to the nucleus of the spiral galaxy NGC 4319.  The filament shows on a four-hour photograph taken with the 200-inch Palomar telescope on 28 March 1971, and on hydrogen-light plates from May 1971.  Its conclusion is that Markarian 205 is connected to the nucleus of a larger galaxy with a lower redshift.  The article uses it as Arp's flagship case, which the article says later evidence resolved against him.

1. 22a.

   Page 3:  “In summary, Markarian 205 appears to be a bonafide quasi-stellar object, which is connected to the nucleus of a larger, lower-redshift galaxy.  Evidence that compact objects with intrinsic, non-velocity redshifts are ejected from galaxies has been presented elsewhere (Arp 1970a).” ↩ ↩

Scranton, Ryan et al.  “Detection of Cosmic Magnification with the Sloan Digital Sky Survey.”  The Astrophysical Journal 633:589–602.  2005.  A measurement paper by a large team of Sloan Digital Sky Survey astronomers, which detects cosmic magnification (the brightening and spreading of distant quasars by the gravity of foreground matter) at 8σ, a statistical confidence far beyond chance, using about 200,000 quasars and 13 million galaxies over 3,800 square degrees of sky.  The authors say the result agrees with predictions from the WMAP concordance cosmology, the standard model of the universe, and they note that earlier attempts to measure this effect had often disagreed with one another.  The article uses it to show that the excess of quasars near bright galaxies has a standard explanation.

1. 23a.

   Section Abstract:  “We present an 8σ detection of cosmic magnification measured by the variation of quasar density due to gravitational lensing by foreground large scale structure.  To make this measurement we used 3800 square degrees of photometric observations from the Sloan Digital Sky Survey (SDSS) containing ~ 200,000 quasars and 13 million galaxies.  Our measurement of the galaxy-quasar cross-correlation function exhibits the amplitude, angular dependence and change in sign as a function of the slope of the observed quasar number counts that is expected from magnification bias due to weak gravitational lensing… Our measurements of cosmic magnification probe scales ranging from 60 h⁻¹ kpc to 10 h⁻¹ Mpc and are in good agreement with theoretical predictions based on the WMAP concordance cosmology.” ↩

López-Corredoira, M., and C. M. Gutiérrez.  “The field surrounding NGC 7603: cosmological or non-cosmological redshifts?”  Astronomy & Astrophysics 421:407–423.  2004.  A follow-up by the same two authors, based on imaging from three campaigns spread over two years, archive Hubble Space Telescope images and spectra of the field around NGC 7603.  They classify the two faint filament objects as HII galaxies, small galaxies with very vigorous star formation, and find the quasar density roughly as expected at the faintness limit of their data.  They calculate about 3 × 10⁻⁹ as the chance of three background galaxies landing on that filament by accident, and the article uses that figure as its headline probability.

1. 24a.

   Section §5.2.2, page 20:  Page numbers of the arXiv preprint.  “Summing up, even in the worst of the cases, we have that the probability to find only one case like the present three background galaxies of the given magnitudes in the filament/arm among all galaxies up to magnitude 14.0 in B-filter is around 10⁻⁵, so we consider that it is justified to talk about 'anomaly'.”  The trials factor, a correction for how many galaxies were searched, is the 3,655 galaxies in SIMBAD with m_B < 14.0. ↩

Bondi, H., and T. Gold.  “The Steady-State Theory of the Expanding Universe.”  MNRAS 108:252–270.  1948.  A paper that asks whether the laws of terrestrial physics can be trusted in cosmology, and argues that an expanding universe can stay stationary only if matter is continuously created.  It takes the universe to be homogeneous and stationary, and claims that all the observational tests it considers agree with the theory.  The paper was received on 14 July 1948.  The article uses it as the origin of the steady-state model's two core ideas: the perfect cosmological principle and a rate of matter creation too small to observe.

1. 25a.

   Page 254:  “This combination of the usual cosmological principle and the stationary postulate we shall call the perfect cosmological principle, and all our arguments will be based on it.  The universe is postulated to be homogeneous and stationary in its large-scale appearance as well as in its physical laws.” ↩

2. 25b.

   Page 266:  “Accordingly we assume that the rate of creation is everywhere about 10⁻⁴³ g. per sec. per cm.³, although variations by a factor of, say 100, are quite permissible.  This rate corresponds to one new atom of hydrogen per cubic metre per 3 × 10⁵ years.  Accordingly we cannot expect the process to be directly observable.”  Page 252:  The summary puts it as:  “continuous creation of matter in space at a rate which is, however, far too low for direct observation.” ↩

Ryle, M., and R. W. Clarke.  “An Examination of the Steady-State Model in the Light of Some Recent Observations of Radio Sources.”  Monthly Notices of the Royal Astronomical Society 122:349–362.  1961.  A 1961 paper by M. Ryle and R. W. Clarke, based on observations made at the Mullard Radio Astronomy Observatory, that compares new counts of faint radio sources with the numbers the steady-state model predicts.  Received 30 January 1961.  The article uses it as the first failure of the steady-state model, since the counts show the distant universe is not like the nearby one.

1. 26a.

   Section Summary, page 349:  “A comparison of these observational results with those predicted by the steady-state model shows a marked discrepancy, the number of sources observed with a flux density in the range 0·5 to 2 × 10⁻²⁶ watts (c/s)⁻¹ m⁻² being at least 3 ± 0·5 times that predicted by the model.  No attempt has been made to select an alternative model to account for the observations, but the results appear to provide conclusive evidence against the steady-state model.”  Page 361:  The same sentence closes the paper. ↩

Schmidt, Maarten.  “Space Distribution and Luminosity Functions of Quasi-Stellar Radio Sources.”  Astrophysical Journal 151:393–409.  1968.  A 1968 paper by Maarten Schmidt that maps how quasi-stellar radio sources (quasars) are spread through space, using sources from the Revised 3C Catalogue.  It introduced the V/V_m test for whether such sources are evenly spread, and found that they are not: their density rises with redshift.  The article uses it for the density of these sources at redshift 1, compared with nearby ones.

1. 27a.

   Section Abstract, page 393:  “The distribution in space is found to be strongly non-uniform.  The space density, in co-moving coordinates, is increasing with redshift z, such that at z = 1 the density is around 150 and 80 times the local (z = 0) density, for q₀ = 0 and q₀ = 1, respectively.  This density increase corresponds to a N(S) relation quite similar to that exhibited by extragalactic radio sources.”  Page 400:  The test itself is defined here.  “The test for uniformity is simply that V/V_m has a uniform distribution from 0 to 1 for the total sample of sources.” ↩

Lerner, Eric J.  “Radio Absorption by the Intergalactic Medium.”  The Astrophysical Journal 361:63–68.  1990.  A research paper written from Lawrenceville Plasma Physics and published in The Astrophysical Journal.  It uses a sample of 237 spiral galaxies and finds that, for a given infrared brightness, a galaxy's radio brightness falls with its distance.  Lerner reads that fall as radio light absorbed by the gas between galaxies.  The paper was received on 19 July 1989 and accepted on 20 March 1990.  The article uses it as the published basis for the plasma claim that the microwave background is made locally and has no direct cosmological significance.

1. 28a.

   Page 67, left column:  “law dictates that for a body of optical depth unity to have a blackbody spectrum, it must be both emitting and absorbing radiation in near equilibrium.  The CBR must therefore originate locally, if radio absorption is strong.  This does not by itself exclude the big bang as the ultimate source of the CBR energy, but it implies that the isotropy and blackbody spectrum of the CBR, long used as primary evidence of the big band [sic], are caused, or at least greatly modified, by the local intergalactic medium, and have no direct cosmological significance.” ↩

McGaugh, Stacy S.  “A Novel Test of the Modified Newtonian Dynamics with Gas Rich Galaxies.”  Physical Review Letters 106:121303.  2011.  A 2011 letter that compares MOND with 47 galaxies dominated by gas, and reports that the data fall where MOND predicts with zero free parameters.  The article uses it for the author's claim that the relation the data follow is unique to MOND, and for the author's own admission that galaxy clusters are a problem for the theory.  Mirror:  arXiv

1. 29a.

   Page 2:  Preprint page numbers.  On the sample of 47 gas-dominated galaxies.  “The data fall precisely where MOND predicts.  This happens with no fitting whatsoever — there are zero free parameters in Fig. 2.  Computing χ² with the slope fixed to 4 and the normalization fixed at the previously determined value of a₀ gives χ² = 44.3 for 46 degrees of freedom for a reduced χ²_ν = 0.96.  If we treat a₀ as a fit parameter and minimize χ² with the slope fixed to 4, we find a₀ = 1.24 ± 0.14 × 10⁻¹⁰ m s⁻².  This is indistinguishable from the previous value, and χ² actually increases because we have added an unneeded degree of freedom:  χ²_ν = 0.99.  If we further treat the slope as an additional free parameter, we find 3.8 ± 0.2.  This does not differ significantly from the MOND prediction of 4, nor does it improve the fit:  χ²_ν = 0.98.” ↩

2. 29b.

   Page 3:  Preprint page numbers.  “The most serious observational problem facing MOND is the dynamics of rich clusters of galaxies.  These appear to weigh more than can be accounted for with the observed baryons even with the modified dynamics.  This residual mass discrepancy is roughly a factor of two in mass.  On the one hand, this is very disturbing — a theory that seeks to eliminate the need for cosmic dark matter itself suffers a missing mass problem.”  The same page continues:  “While some of the mass in clusters appears to be dark, even in MOND, there is nothing that requires this unseen mass to be in some new form of non-baryonic particle.  Indeed, big bang nucleosynthesis implies the existence of considerably more baryons than have so far been detected.  If only a fraction of these missing baryons reside in clusters it would suffice to resolve the residual mass discrepancy suffered by MOND.” ↩ ↩

McGaugh, Stacy S.  “MOND Prediction for the Velocity Dispersion of the 'Feeble Giant' Crater II.”  ApJ Letters 832:L8.  2016.  A 2016 letter, posted as an arXiv preprint on 19 October 2016, that predicts the velocity spread of stars in the faint galaxy Crater II before anyone had measured it.  The prediction rests on MOND's external field effect, the pull of the Milky Way strong enough to change the galaxy's own dynamics, and it gives about 2 km/s where a galaxy isolated from the Milky Way would show about 4.  The article uses it as its clearest example of a prediction made in advance.  Mirror:  arXiv

1. 30a.

   Section 4.3, page 5:  Preprint page numbers.  “Barring a drastic failure of the input data and necessary assumptions, the velocity dispersion of Crater II must be σ_efe ≈ 2 km s⁻¹.  It should not be 4 km s⁻¹ as it would be if Crater II were isolated.  It certainly should not be significantly larger:  a high observed velocity dispersion would falsify MOND.” ↩

Caldwell, Nelson et al.  “Crater 2: An Extremely Cold Dark Matter Halo.”  ApJ 839:20.  2017.  A spectroscopic study of Crater 2, a satellite of the Milky Way, which identified about 62 members among 390 candidate stars.  It measured their velocity spread at 2.7 km/s, the coldest of any dwarf galaxy resolved so far, and was posted to arXiv on 19 December 2016, two months after McGaugh's prediction.  The article uses it as the measurement that fell inside MOND's predicted band.

1. 31a.

   Section Abstract:  “We present results from MMT/Hectochelle spectroscopy of 390 red giant candidate stars along the line of sight to the recently-discovered Galactic satellite Crater 2… we identify ∼62 members of Crater 2, for which we resolve line-of-sight velocity dispersion σ_vlos = 2.7 +0.3 −0.3 km s⁻¹… Despite Crater 2's relatively large size (projected halflight radius R_h ∼ 1 kpc) and intermediate luminosity (M_V ∼ −8), its velocity dispersion is the coldest that has been resolved for any dwarf galaxy.  These properties make Crater 2 the most extreme low-density outlier in dynamical as well as structural scaling relations among the Milky Way's dwarf spheroidals.” ↩

Clowe, Douglas et al.  “A Direct Empirical Proof of the Existence of Dark Matter.”  ApJ Letters 648:L109–L113.  2006.  A 2006 weak-lensing study of 1E0657-558, a pair of galaxy clusters that collided.  It maps the mass from the way it bends light, using ground-based and Hubble images, and finds that the mass sits with the galaxies rather than with the X-ray-emitting plasma, the largest share of ordinary matter in the system, an offset of 8σ.  The article uses it as the direct test that changing the gravity law cannot explain that offset.

1. 32a.

   Section Abstract:  “An 8σ significance spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law, and thus proves that the majority of the matter in the system is unseen.” ↩ ↩

Lovyagin, Nikita et al.  “Cosmological Model Tests with JWST.”  Galaxies 10(6):108.  2022.  A 2022 journal article that runs the "angular diameter—redshift" test on the first JWST observations, which compares how large distant galaxies look with how far away they are.  It compares the standard model with static models, including Zwicky's tired-light model, and says tired light is currently assumed to be ruled out but challenges that assumption.  The article cites it as a 2022 static-universe analysis that challenges the assumption that tired light is ruled out.

1. 33a.

   Page 14, section §4:  “Another important distinctive parameter is the cosmological time dilation.  It can be used for determining the nature of the cosmological redshift.  For example, the static cosmological model with photon-energy dissipation predicts no time dilation.  Whereas the FRLW models and the static models with the cosmological redshift of the general-relativistic (gravitational) nature predict the time-dilation factor scaling with the factor of (1 + z).  The time-dilation effect is actually observed in the light-curves of the type-Ia supernovae, which strongly supports the expanding-Universe models or the static-Universe models of the Einstein-de-Sitter type.” ↩ ↩

2. 33b.

   Pages 14–15, section §4:  “Although our analysis of JWST observations favours a static (TL) model of the Universe rather than the standard (expanding-Universe) cosmology, the latter is strongly supported by other observational evidence.  The main challenges which any static cosmological model must face are the cosmic microwave background (CMB), the abundance of chemical elements in the Universe and the formation of cosmic structure.” ↩

Barnes, Luke A.  “Size of Galaxies in JWST Data and Cosmology — Reply to Lisle.”  Answers Research Journal 17:785–789.  2024.  A reply to Lisle in the same journal, written by Luke A. Barnes of Sydney, Australia.  Barnes ran a standard galaxy-formation simulation (the SAGE model, run through the free TAO web tool) and found that its predicted galaxy sizes are consistent with the JWST data, including data above redshift z = 7.  He says the apparent conflict comes from Lisle's own model, which gives every galaxy one size at all times, and the article uses it for Barnes's claim that Lisle's Doppler model is the same as an expanding-space model described in other coordinates, and for his point that the Doppler model gives no young universe.

1. 34a.

   Page 788:  “Thus, the 'Doppler Model' of Lisle (2024) is physically indistinguishable from an expanding space model.  It is a mere redescription.  The only difference is a change of coordinates, which aren't physically observable.” ↩

2. 34b.

   Page 788:  “In both the Doppler Model and the standard model, the finite speed of light will make the universe appear to be billions of years old, so supporting the first while criticising the second does nothing to solve the Starlight and Time problem.” ↩

3. 34c.

   Page 788:  The sentences that follow the one on the Starlight and Time problem, in the same paragraph.  “Lisle proposes to solve this with the Anisotropic synchrony convention, which implies that we see galaxies as they are now, regardless of how far away they are.  This gives the model enough freedom that any observed population of galaxies is consistent with a young universe.  In that case, one might as well attach the convention to the Big Bang model and be done with it.” ↩

Naidu, Rohan P. et al.  “A Cosmic Miracle: A Remarkably Luminous Galaxy at z_spec = 14.44 Confirmed with JWST.”  The Open Journal of Astrophysics.  2026.  An observational paper confirming the redshift of MoM-z14, a luminous galaxy, from a sharp Lyman-α break in JWST NIRSpec spectra, a drop in its ultraviolet light caused by hydrogen absorption.  The article cites it as the most distant spectroscopically confirmed galaxy, at redshift 14.44, and uses that redshift in its check of Lisle's own equations for the age of the universe.  Mirror:  arXiv ↩

Mills, B. Y., and O. B. Slee.  “A Preliminary Survey of Radio Sources in a Limited Region of the Sky at a Wavelength of 3.5 m.”  Australian Journal of Physics 10:162–194.  1957.  A 1957 survey of radio sources at a wavelength of 3.5 m, made in Sydney, that checked its own list against the Cambridge survey.  Its authors worked out that the Cambridge list is reliable only above a certain flux density, and that agreement between the two surveys breaks down below it.  The article uses it to show that the first version of the radio-source argument, which relied on the Cambridge catalogue, was wrong.

1. 36a.

   Section §V, Analysis of the Sydney Catalogue (opening), page 174:  “It has been shown that the Cambridge catalogue does not agree with ours and that errors in the former due to poor resolution might be expected to occur just at the level where agreement begins to break down.  On the other hand, the corresponding level of reliability in our catalogue is nearly 10 times lower at a flux density of 8 × 10⁻²⁶ W m⁻² (c/s)⁻¹.”  Page 179:  On their own source counts:  “the slope of the straight portion which, being three probable errors greater than −1·5, suggests a possible cosmological effect;  it is necessary to estimate the contribution of instrumental effects to this increased slope.” ↩

Hoyle, F. et al.  “Note on a Comment by Edward L. Wright.”  arXiv.  Dec 14, 1994.  A four-page reply by the three authors of the quasi-steady-state model (a steady-state model whose expansion pulses up and down) to Edward Wright's criticism of their radio-source counts, not published in a journal, and its own reference list cites Wright's critique as "Wright, E.L. 1994, preprint."  The authors say the model's free parameters can be re-chosen to fit the data, and they ask why standard cosmology needs radio sources to evolve so sharply in the recent past.  The article uses both points.

1. 37a.

   Page 3:  “As we have said elsewhere the QSSC is based on a fundamentally new idea involving matter creation in an oscillatory mode imposed on an expanding universe. … The exact values of the free parameters of the theory are not known.  The points in dispute are related to the numerical values we have chosen when we compare with observational details.  Suitable choices can and do make the theory compatible with the observations, i.e. it is obvious that the theory is not disproved by Wright's analysis of the data.” ↩

Alfvén, Hannes.  Plasma physics, space research and the origin of the solar system.  Pages 306–316.  Dec 11, 1970.  Alfvén's Nobel Lecture of 11 December 1970, on how the Solar System formed.  It argues that plasma physics is fundamental to understanding the Solar System's origin, and that the first approach to cosmic plasma physics has been a failure in several important cases.  The article uses it for Alfvén's own verdict on cosmic plasma physics and for the two approaches he set side by side.

1. 38a.

   Page 308:  “The cosmical plasma physics of today is far less advanced than the thermonuclear research physics.  It is to some extent the playground of theoreticians who have never seen a plasma in a laboratory.  Many of them still believe in formulae which we know from laboratory experiments to be wrong.  The astrophysical correspondence to the thermonuclear crisis has not yet come.” ↩

McGaugh, Stacy S. et al.  “The Radial Acceleration Relation in Rotationally Supported Galaxies.”  Physical Review Letters 117:201101.  2016.  A 2016 letter that reports a tight relation, across 153 rotating galaxies, between the acceleration traced by their rotation and the acceleration predicted from the observed ordinary matter alone.  Its 2693 data points follow one relation with small scatter, which the authors say is largely caused by measurement uncertainty, and they call the relation a natural law for rotating galaxies.  The article uses it as the source of the best modern measurement of MOND's acceleration constant, and for its point that the scatter is about the size of the measurement errors.  Mirror:  arXiv

1. 39a.

   Section Abstract:  “We report a correlation between the radial acceleration traced by rotation curves and that predicted by the observed distribution of baryons.  The same relation is followed by 2693 points in 153 galaxies with very different morphologies, masses, sizes, and gas fractions.  The correlation persists even when dark matter dominates.  Consequently, the dark matter contribution is fully specified by that of the baryons.  The observed scatter is small and largely dominated by observational uncertainties.  This radial acceleration relation is tantamount to a natural law for rotating galaxies.” ↩

2. 39b.

   Page 3:  Preprint page numbers.  “For our adopted Υ⋆, we find g^† = 1.20 ± 0.02 (random) ± 0.24 (systematic) × 10⁻¹⁰ m s⁻².” ↩

Lewis, Geraint F., and Brendon J. Brewer.  “Detection of the Cosmological Time Dilation of High Redshift Quasars.”  Nature Astronomy 7:1265–1269.  2023.  A 2023 paper that reports cosmic time dilation (distant events appear to unfold more slowly) in 190 quasars, each monitored for over two decades in several wavebands.  It assesses its hypotheses with Bayesian analysis, a method that weighs each one by how well it fits the data.  The article quotes its claim that this counters earlier reports that quasar variability lacked the expected time dilation.  Mirror:  arXiv

1. 40a.

   Section Abstract:  “Whilst observations of cosmological supernovae unambiguously display the expected redshift-dependent time dilation, this has not been the case for other distant sources.  Here we present the identification of cosmic time dilation in a sample of 190 quasars monitored for over two decades in multiple wavebands by assessing various hypotheses through Bayesian analysis.  This detection counters previous claims that observed quasar variability lacked the expected redshift-dependent time dilation.” ↩

Brewer, Brendon J. et al.  “Revisiting the Cosmological Time Dilation of Distant Quasars: Influence of Source Properties and Evolution.”  Monthly Notices of the Royal Astronomical Society 537(2):809–816.  2025.  A reanalysis of the 2023 quasar result that adds source properties and evolution to the model, and finds that an intrinsic scatter in the variability timescales, which the earlier analysis did not consider, is favoured by the data.  It still finds the cosmological signal, with exponent n = 1.14 ± 0.34, which the authors say is consistent with relativistic cosmologies.  The article uses it as a follow-up in which the 2023 authors, with Yuan Li, tested their own result.  Mirror:  arXiv

1. 41a.

   Section Conclusions:  “Despite these adjustments, we still detect the cosmological signal (albeit with slightly increased uncertainty), finding that a cosmological dependence of the form (1 + z)ⁿ yields n = 1.14 ± 0.34, consistent with the expectations from relativistic cosmologies.  We compared our modelling assumptions against several alternatives and demonstrated that our main model was favoured over most others using a Bayesian model comparison approach.  The only exception was a model that assumes n = 1, which outperformed the main model.”  Section Abstract:  The abstract adds that.  “a significant intrinsic scatter of 0.288 ± 0.021 dex in the variability timescales, which was not considered in the previous analysis, is favoured by the data.” ↩

Walsh, D. et al.  “0957 + 561 A, B: twin quasistellar objects or gravitational lens?”  Nature 279:381–384.  May 31, 1979.  A report in Nature on two quasars 5.7 arc seconds apart, whose spectra leave little doubt that they are associated.  The authors discuss whether they are two distinct objects or two images of one quasar made by a gravitational lens, a massive object whose gravity bends light.  The article uses it as the first case of this kind, found in 1979.

1. 42a.

   Section Abstract:  “0957 + 561 A, B are two QSOs of mag 17 with 5.7 arc s separation at redshift 1.405.  Their spectra leave little doubt that they are associated.  Difficulties arise in describing them as two distinct objects and the possibility that they are two images of the same object formed by a gravitational lens is discussed.” ↩

Angus, Garry W.  “Is an 11 eV sterile neutrino consistent with clusters, the cosmic microwave background and modified Newtonian dynamics?”  MNRAS 394:527–532.  2009.  A theory paper asking whether one sterile neutrino of about 11 eV could solve MOND's outstanding problems, on the scale of clusters and on the scale of the microwave background.  Its model is flat, with the neutrino density parameter Ω at about 0.23, and has the same expansion history as the standard model, ΛCDM.  The article uses it as the MOND cosmology that matches the microwave background, by adding a hot dark matter component.

1. 43a.

   Section Abstract:  “If a single sterile neutrino exists such that m_νs ∼ 11 eV, it can serendipitously solve all outstanding issues of the Modified Newtonian Dynamics.  With it one can explain the dark matter of galaxy clusters without influencing individual galaxies, match the angular power spectrum of the cosmic microwave background and potentially fit the matter power spectrum.  This model is flat with Ω_νs ∼ 0.23 and the usual baryonic and dark energy components, thus the Universe has the same expansion history as the ΛCDM model and only differs at the galactic scale where the Modified Dynamics outperforms ΛCDM significantly.” ↩ ↩

Hartnett, John G.  “The Carmeli metric correctly describes spiral galaxy rotation curves.”  arXiv:gr-qc/0407082.  Jul 22, 2004.  A preprint by John G. Hartnett of the University of Western Australia (version 6 is dated 4 April 2005), arguing that Carmeli's extension of general relativity explains spiral galaxy rotation without dark matter.  It derives the Tully-Fisher relation, the link between a galaxy's mass and the fourth power of its rotation speed, from the theory's own equations, and fits the rotation curve of NGC 6503.  The article uses it for the theory's characteristic acceleration and for Hartnett's claim that the theory gives the Tully-Fisher relation without dark matter.

1. 44a.

   Section §I:  “Hence the latter is consistent with Milgrom's phenomenological approach in the low acceleration limit.”  Section §IV:  “(2/3)a₀ ≈ 5.2 × 10⁻¹⁰ m s⁻², depending on the precise value of τ.” ↩

2. 44b.

   Section §I:  “As a consequence a universal constant a₀ (in this case, slightly different to Milgrom's) is introduced as the minimum acceleration in the cosmos.” ↩

Carroll, Sean.  “Doubt and dissent are not tolerated.”  Preposterous Universe.  May 29, 2004.  A blog post by Sean Carroll replying to an online petition, first published in New Scientist, that complained of the terrible dominance of the Big Bang model.  The article uses it for Carroll's list of Big Bang predictions that came true, his answer to Eric Lerner's energy argument, and his remark that young people who doubt the Big Bang are unlikely to get permanent jobs at research universities.

1. 45a.

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

Tsymbal, V. V. et al.  Cosmological Observational Tests in the JWST Era. II: The Tolman Test.  Apr 30, 2026.  A preprint, not peer reviewed at the time of writing, that tests the Tolman surface-brightness prediction on 6 860 JWST galaxies with spectroscopic redshifts.  The article notes that this group has argued for static cosmologies before, and that a preprint is not a result.

1. 46a.

   Section abstract:  “We analyzed 6 860 galaxies with reliably determined spectroscopic redshifts from the ASTRODEEP-JWST photometric catalogue.  We find that (a) the mean surface brightness of galaxies indeed decreases with increasing distance, and (b) the observed trend shows a significant departure from the prediction of the standard cosmological model, which expects the mean surface brightness to decline as ~ (1 + z)^-4.” ↩

Lerner, Eric J.  “Observations contradict galaxy size and surface brightness predictions that are based on the expanding universe hypothesis.”  Monthly Notices of the Royal Astronomical Society 477(3):3185–3196.  2018.  A 2018 paper by Eric J. Lerner, published in Monthly Notices of the Royal Astronomical Society, on the sizes and surface brightnesses of galaxies.  The article calls it Lerner's one refereed astronomy paper since 2004.

1. 47a.

   Section Abstract:  “We show that the radii data for both disc and elliptical galaxies are incompatible with any of the published size-evolution predictions based on an expanding universe.”  Twenty-seven citations as of August 2026, mostly in alternative-cosmology venues, and no published rebuttal.  His widely circulated JWST claim appeared in IAI News (11 August 2022), a magazine, not a journal. ↩

Cirelli, Marco et al.  Dark Matter.  Oct 31, 2025.  A 524-page review of dark matter.  Its chapter 11, "Alternatives to Dark Matter," covers MOND, including the 1984 Bekenstein and Milgrom version and a relativistic model by Skordis and Złośnik.  The article uses it for two points: that the bare MOND formula is not a consistent theory, and that the scalar field in a relativistic MOND model can play the role of dark matter in cosmology.

1. 48a.

   Page 401:  “The present situation is confusing;  while some authors that analysed the Gaia data claim that wide binaries agree with the Newtonian dynamics, and thus exclude MONDian effects with up to 19σ significance (see Banik et al. (2023)), others instead claim a discovery of MONDian anomalies with a significance of up to 10σ, and thus an exclusion of Newtonian dynamics (see Chae (2023)).  The main issue is that some wide binaries involve a third unseen object, that produces MONDian-like deviations from Newtonian gravity.” ↩

Marra, Valerio et al.  “A fundamental test for MOND.”  MNRAS 494:2875–2885.  2020.  A 2020 journal paper that repeats a test of whether galaxies share one fundamental acceleration constant, a0, and finds that a shared constant is incompatible with the data at more than 5σ.  Rodrigues, a co-author here, led the 2018 version, and this paper replaces its Gaussian approximations with a Monte Carlo simulation, a method that builds the statistics from many random trials.  The article uses it because the same sample gives 26σ, 14σ and 5.3σ under three statistical treatments, which shows how much the result depends on method.  Mirror:  arXiv

1. 49a.

   Section Conclusions, page 9:  Preprint page numbers.  “In this way, we have confirmed that there is a strong evidence against a common a₀ value:  a fundamental acceleration scale a₀ is rejected at more than 5σ.” ↩

Narlikar, J. V., and T. Padmanabhan.  “Standard Cosmology and Alternatives: A Critical Appraisal.”  Annual Review of Astronomy and Astrophysics 39:211–248.  2001.  A review article that appraises standard cosmology and its alternatives, including the quasi-steady-state model, by J. V. Narlikar and T. Padmanabhan.  The article calls both authors the model's own, and uses the review because it concedes that the model has major weaknesses and cannot yet make clear predictions.

1. 50a.

   Quoted at second hand, as the article says.  The wording is Kragh's report of the review in arXiv:1201.3449, p. 25, and Kragh gives the locators as p. 239 and p. 246.  “In a refreshingly self-critical review Narlikar and T. Padmanabhan refer to 'the snowball effect arising from the social dynamics of research funding,' but they also admit major methodological and technical weaknesses in QSSC.  The model 'lacks the simplicity and beauty of the original steady state model' and 'cannot continue to survive and hope to make an impact based purely on the shortcomings of SC [the standard cosmology].'  It needs to be developed to such a level that it can make clear predictions rather than provide post facto explanations for already observed phenomena.” ↩