Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn

Rajendra P. Gupta

REVIEW 4 major objections 4 minor 199 references

Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn

T0 review · 4 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read The paper claims that JWST's 'impossible' early galaxies become ordinary once the observed redshift is split between cosmic expansion and tired light.

desk verdict Application of CCC+TL to JWST size/mass/density tensions—new transfer functions and worked examples, but the size effect rests on a tired-light component partly fitted to the same data and the luminosity derivation has a fixable algebra error. read the letter →

arxiv 2510.13844 v1 pith:XEKXVJQE submitted 2025-10-11 physics.gen-ph

Rajendra P. Gupta This is my paper · ORCID

classification physics.gen-ph

keywords galaxyevolutionhigh-redshiftgalaxiesearlyuniversetiredlightcovaryingcouplingconstantsangulardiameterdistanceJWSTsize-mass-densityrelation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the JWST-era puzzle—galaxies at cosmic dawn that look too massive, too compact, too dense, and too early to have formed—is an artifact of assuming all redshift comes from cosmic expansion. Reinterpreting the same observations in a cosmology where fundamental constants co-vary and a tired-light component shares the redshift, the angular-diameter distance grows much faster with redshift. As a result, inferred galaxy radii increase as (1+z)^0.93, dynamical masses scale up, number densities fall by up to (1+z)^-2.80, and the early universe is about ten times older near z=10. The paper concludes that early galaxies and little red dots no longer require exotic formation channels such as super-Eddington black hole growth.

What carries the argument

The carrying mechanism is the CTL angular-diameter distance relation d_A(z) = f(z_x)d_p(z_x)/(1+z), built from the redshift split (1+z)=(1+z_x)(1+z_t). Equating the proper distance traveled by a photon under the two redshift causes fixes the split without extra free parameters, and the extra f(z_x) factor makes d_A grow much faster than the ΛCDM angular-diameter distance at z>1. That single ratio drives all the paper's derived corrections: size scales as (d_Ax/d_AΛ), luminosity scales as d_A^2 with additional redshift factors, dynamical mass scales with size, and densities scale as inverse powers of size.

What would settle it

A decisive test is the distance-duality relation: measure luminosity distances from standard candles and angular-diameter distances from independent geometric probes at z≈1–3 and beyond. CTL predicts a specific deviation because time dilation and photon energy loss apply only partly to the expansion redshift; if the standard relation d_L=(1+z)^2 d_A holds, the tired-light split—and with it the (1+z)^0.93 size enlargement—is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the observed redshift z should be factored as (1+z)=(1+z_x)(1+z_t), with z_x from expansion and z_t from tired light, and that the angular-diameter distance in this CTL model, d_A = f(z_x)d_p(z_x)/(1+z), rises far more steeply than in ΛCDM. Because an object's physical size is d_A times its observed angular size, all galaxies and little red dots become larger as redshift increases—by a factor of about (1+z)^0.93 compared with ΛCDM estimates. The same enlargement raises dynamical masses, lowers surface/volume/number densities, and, together with the model's slower aging, stretches the time available for galaxy assembly. The paper presents ratios of size, luminosity,

Load-bearing premise

The load-bearing premise is that tired light is real and contributes to the observed redshift, splitting it cleanly into an expansion part and a tired-light part; the paper states the mechanism is currently unknown, and the model was introduced partly because CCC alone failed the JWST size data.

Editorial extensions

If this is right

The JWST galaxy JADES-GS-z14-0, with a ΛCDM UV radius of about 260 pc at z=14.18, would have a radius of about 3.2 kpc in the CTL model; compact early galaxies are not inherently compact.
Dynamical masses of high-redshift galaxies are substantially higher while stellar masses rise only modestly (factor ~1.7 at z=14), so the stellar-to-dynamical mass ratio drops for that galaxy from ~2 to ~1/14, consistent with gas-dominated young systems.
Number densities of quiescent and ultra-massive galaxies drop by factors of hundreds at z~5–7, aligning observed abundances with model predictions rather than exceeding them by 100–1000 times.
At z=10 the model gives the universe roughly ten times more time than ΛCDM; a 280 Myr-old universe at z=15 becomes 4.35 Gyr, removing the need for unrealistically rapid star formation and super-Eddington black hole accretion.
Luminosity and stellar-mass corrections are small (a factor up to ~1.8 at z=20), so the model identifies size, not brightness, as the main resolution of the early-galaxy tension.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same redshift split implies a testable violation of the standard distance-duality relation d_L=(1+z)^2 d_A; a high-redshift measurement comparing standard-candle distances with geometric or angular-diameter distances could confirm or kill the tired-light component.
The (1+z)^0.93 correction is universal in this model, so it can be applied to published size-mass evolution slopes: any survey fitted with r_e ∝ (1+z)^s should show s+0.93 if CTL is right, a prediction existing JWST catalogs can check immediately.
If the model's enlarged radii are correct, gas fractions and star formation efficiencies inferred from dynamical-to-stellar mass ratios at z>5 will be much higher than currently reported, shifting interpretations of early metal enrichment.
Because the tired-light mechanism is unspecified, the size correction is currently a phenomenological rescaling; a physical derivation of the TL component would turn these ratios into quantitative predictions about photon interactions over cosmological distances.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The headline is a straightforward application of Gupta's CCC+TL cosmology to JWST-era galaxy size/mass/density tensions. The transfer functions themselves—size exponent +0.93, dynamical mass scaling with R, number density scaling with R^-3, and the mild luminosity correction—are new relative to his earlier papers, and the worked examples (GS-z14, RUBIES-UDS-QG-z7, GN-72127) make the implications concrete. If one accepts the CTL angular-diameter-distance ratio, the arithmetic mostly follows.

The trouble is on the input side. The size enlargement is entirely carried by the tired-light redshift split, and the paper admits (Section 2, ref. [86]) that TL was invoked precisely because CCC alone failed to fit the JWST size data at cosmic dawn. So the headline effect is not an independent prediction; it is partly calibrated to the same anomaly it is used to dissolve. The paper is transparent about this, which I credit, but it should not be framed as a falsification test.

There is also a concrete derivation error. Eq. (12) puts (1+z_t) in the numerator; flux conservation puts it in the denominator, and Eq. (14) is the corrected denominator form. A reader following the printed equations cannot reproduce the luminosity ratios or the claimed factor 1.8 at z=20. That is likely a typo, but it is in a load-bearing spot and must be fixed. In the same spirit, the model parameters α and H0 are not given here, so the 0.93 exponent and Table 1's conversion factors cannot be checked without digging through earlier papers. The author should report them.

The paper does several things well. It is clearly written, engages a wide range of relevant JWST/ALMA results, and separates the age-stretch effect from the distance-ratio effects. The age argument—roughly a dex more time at z~10—is logically independent of the TL split and is the part I would want to see developed further. The density examples are also useful illustrations of how a different dA(z) would change the inferred compactness of little red dots.

I would not cite this paper in my own work in the next year, and I would not take its quantitative claims at face value without the fixes above. But it is a serious, readable statement of an alternative-cosmology position, and the JWST tensions it addresses are real. Send it to a referee who knows both the size data and alternative cosmologies; it deserves referee time, with the expectation of major revision.

Referee Report

4 major / 4 minor

Summary. The paper argues that the CCC+TL cosmology—an alternative to ΛCDM with covarying coupling constants and a tired-light component—predicts larger angular-diameter distances at high redshift, and hence larger physical sizes, lower inferred densities, and modestly higher luminosities for galaxies observed by JWST. It derives ratios for size, luminosity/mass, and density relative to ΛCDM, fits the size ratio as r_e ∝ (1+z)^0.93, and applies the scalings to specific objects (JADES-GS-z14-0, Abell2744-QSO1, Little Red Dots, RUBIES-UDS-QG-z7). It concludes that the early-galaxy tensions in ΛCDM are largely resolved in CTL.

Significance. If the CTL model is taken as given, the size-enlargement result follows directly from the ratio d_A^CTL/d_A^Λ and is a useful consistency check for the model. The paper is clearly organized and compiles many current JWST results, making concrete quantitative predictions that can in principle be checked. However, its quantitative claims for luminosity, stellar mass, and number density are compromised by an algebraic error and missing model parameters, and the central size effect relies on the tired-light split that was introduced specifically to address JWST galaxy sizes, making the 'prediction' partly circular. The paper's strengths—clear structure, specific applications, and acknowledgment of the unknown TL mechanism—do not outweigh these issues.

major comments (4)

[Section 3, Eqs. (12) and (14)] The derivation chain for the luminosity ratio is internally inconsistent. Equating fluxes before Eq. (12) gives L_Λ/d_pΛ^2 = L_x (1+z_t)/d_px^2, which implies L_x = L_Λ (d_px^2/d_pΛ^2)/(1+z_t); the printed Eq. (12) has (1+z_t) in the numerator. Equation (14), used for Figure 3 and Table 1, matches the corrected denominator version (with (1+z_t)^3). Thus a reader following the printed equations cannot reproduce the luminosity ratios, and the figures/table rely on an unstated correction. Please fix Eq. (12) and re-verify all quoted luminosity and stellar-mass ratios, including the abstract's luminosity factor 1.8 at z=20.
[Section 2, Eqs. (8)–(11) and Figure 1] The CTL angular-diameter distance—and therefore the central r_e ∝ (1+z)^0.93 result, the density scalings, and every entry in Table 1—depends on the model parameters α, H0, and the resulting z_x(z) and f(z_x) split. None of these are given in this paper. Without them, the curves in Figures 1–5, the exponent 0.93, and the numerical factors in Table 1 cannot be independently checked. Please provide the fitted parameter values, a formula or table for z_x(z), and the numerical form of f(z_x), or a clear pointer to a publicly available implementation.
[Section 2, paragraph after Eq. (11); Section 4] The tired-light component is load-bearing for the size enlargement—without it the (1+z)^0.93 correction disappears—but the text states that TL was invoked in ref. [86] only after CCC alone was 'unsatisfactory in explaining the JWST galaxy size data at cosmic dawn,' and that the TL mechanism is 'currently unknown.' The agreement with JWST sizes is therefore partly an accommodation of the target data rather than an independent prediction. Please clearly separate 'accommodated' from 'predicted' and suggest out-of-sample tests (e.g., CMB spectral distortions, redshift drift, or surface-brightness tests) that do not use the data that motivated the TL admixture.
[Section 3 'Density Decrease' and abstract 'number density by (1+z)^{-2.80}'] The paper applies the object-volume scaling d_A^{-3} to the number density of galaxies in surveys (e.g., the factor ~385 at z=7 for RUBIES-UDS-QG-z7, and the abstract's exponent -2.80). For survey number densities, the relevant volume element is the comoving volume element, which scales as D_M^2 (dχ/dz), not simply as d_A^3. The two are equal only under additional assumptions about how the line-of-sight distance changes. Please derive the number-density modification from the CTL metric volume element and state whether the quoted factors are physical-volume or comoving-volume densities.

minor comments (4)

[Section 4] The phrase 'the question becomes mute' should read 'the question becomes moot.'
[Figures 1–5] The figures give no indication of the parameter values, the numerical integration used, or uncertainties. Adding a short caption note or appendix with the parameter values would greatly improve reproducibility.
[Section 4, Table 1] The table ignores uncertainties, which is acceptable for illustration, but the caption should state this explicitly. Also, the 'Number den. LRD' row appears to be a placeholder rather than a computed value; please clarify.
[References] There are a few typographical issues in the reference list (e.g., ref. 113, 'misión' for 'mission'). A careful proofread is recommended.

Circularity Check

2 steps flagged · score 7.0 of 10

The claimed r_e∝(1+z)^{0.93} correction is a restatement of the tired-light ansatz introduced in ref. [86] to fit the same JWST size data it is used to reinterpret.

ansatz smuggled in via citation [Section 2, paragraph following Eq. (11); also TL limitations paragraph]
"It was shown in an earlier paper [86] that while the CCC and the ΛCDM models are great in fitting the low redshift observations, e.g., Pantheon+ supernova type Ia data, both of them are unsatisfactory in explaining the JWST galaxy size data at cosmic dawn and reionization redshifts. We then invoked the tired-light (TL) concept of Zwicky [85] to coexist in the expanding Universe."

The size enlargement used throughout the paper is the CTL/ΛCDM angular-diameter-distance ratio, with d_Ax = d_px f(z_x)/(1+z_x) and (1+z)=(1+z_x)(1+z_t) (Eqs. 11-13). The TL split is the ingredient that makes d_Ax grow faster than d_AΛ; the paper acknowledges CCC alone was unsatisfactory for JWST sizes and that TL's mechanism is 'currently unknown.' Thus the TL component was adopted in ref. [86] to accommodate the same JWST angular-size data whose tension this paper reinterprets as a predicted r_e∝(1+z)^{0.93} correction. The central result is therefore a restatement, via self-citation, of an ansatz chosen to fit the target phenomenon rather than an independent first-principles prediction.
self definitional [Section 4, 'Size Evolution' paragraph; Section 3, 'Size Increase']
"We also show the inverse of the power-law fit, 𝑅𝑒 = (1 + 𝑧)0.93, for the increase in the physical size of the objects in the CTL (labeled as CCC+TL) model compared to the ΛCDM model."

Section 3 defines the size increase as 'taking the ratio of d_A in the CTL and ΛCDM models,' and physical size is proportional to d_A by definition. The quoted 0.93 exponent is described as the inverse of a power-law fit to that model-generated ratio curve. Consequently r_e∝(1+z)^{s+0.93} is a summary of the definitional d_A ratio, not a parameter-free observable prediction. Combined with the TL ansatz imported from [86], the corrected size evolution is forced by the model input rather than tested against it.

full rationale

The paper's corrections are computed from the ratio of the CTL and ΛCDM angular-diameter distances; this is an algebraic consequence of Eqs. (11)-(13), not an independently measured or simulated result. The paper explicitly states that the tired-light component was introduced in prior work [86] only after CCC and ΛCDM both failed to explain the JWST galaxy size data, and that the TL mechanism is 'currently unknown.' Since that TL split is exactly what makes d_Ax/d_AΛ grow with z, the headline 'size increase' r_e∝(1+z)^{0.93} restates the model choice made to fit the target data; the exponent is a fit to the model's own ratio curve. The consistency claims (Pantheon+, BAO, CMB, etc.) are carried by self-citations [86-89] rather than demonstrated in this paper. Separately, the printed luminosity derivation is internally inconsistent: Eq. (12) places (1+z_t) in the numerator while Eq. (14) requires it in the denominator, so the luminosity/mass corrections cannot be reproduced from the paper's equations as written; this is a correctness problem, not counted as circularity. On the circularity axis, the central claim reduces to an ansatz adopted to fix the same anomaly it is used to explain, giving score 7.

Assumptions & free parameters 2 free parameters · 6 assumptions · 2 invented entities

The rescaling calculation depends almost entirely on the prior CCC+TL model: the exponential form of f(t), the TL redshift split, and the modified Friedmann equations. The free parameter α is fitted to Pantheon+ data in earlier papers and is not given here. No new entity has independent evidence outside the model itself.

free parameters (2)

α (CCC coupling evolution constant) = not stated in this paper
Defines f(t)=exp(α(t−t0)); enters H(z), proper distance, and hence all angular-diameter-distance rescaling exponents.
H0 (Hubble constant in CTL) = not stated in this paper
Together with α sets the angular-diameter-distance scale; obtained from the Pantheon+ fit in previous works by the same author.

assumptions (6)

domain assumption Coupling constants covary as c∝f(t), G∝f(t)^3, ℏ∝f(t)^2, kB∝f(t)^2.
Adopted from ref [84] (same author); no derivation in this paper; underlies the modified Friedmann equations (Eqs 2–4).
ad hoc to paper f(t)=exp(α(t−t0)) with α an unknown constant.
Chosen 'to be consistent with Occam's razor'; not derived; central to H(z), d_p, and d_A.
domain assumption Tired light contributes to the observed redshift alongside expansion, with (1+z)=(1+z_x)(1+z_t), and the proper distance traversed is the same for both effects.
Invoked in Section 2 following Eq (11); mechanism unknown and acknowledged in the text; drives the d_A enhancement that produces the size correction.
domain assumption Flat, matter-dominated universe with Ωr≪Ωm and no dark energy.
Used to simplify Eq (7) to Eq (8); not central to the ratio comparison but assumed throughout.
domain assumption Mass-to-light ratio Y* ≡ M*/L is constant.
Explicitly assumed in Section 3 before 'Mass Increase'; if false, the stellar-mass rescaling is not simply L_x/L_Λ.
domain assumption Modified Einstein equations from Costa et al. and the author's prior papers are valid and general covariance can be maintained.
Section 2 addresses covariance by citing refs [129–132] but does not demonstrate it in this paper.

invented entities (2)

Tired-light photon-energy-loss mechanism
purpose: Produces the TL redshift component z_t and yields the d_Ax growth relative to ΛCDM, which is the basis for the size/mass/density corrections.
The paper states 'It is currently unknown and the subject of ongoing research'; no independent falsifiable handle is presented.
Covarying coupling function f(t) with G∝f^3, c∝f, etc.
purpose: Modifies the FLRW metric and Friedmann equations, stretching distances and ages.
No direct measurement of a varying G or c is provided; the paper argues existing constraints are invalid because other constants were held fixed.

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Cite this review

Pith. "Pith review of Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn." pith.science (2026). https://pith.science/paper/XEKXVJQE

@misc{pith2026251013844,
  author       = {Pith},
  title        = {Pith review of: Evolution of Size, Mass, and Density of Galaxies Since Cosmic Dawn},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XEKXVJQE}},
  note         = {Machine review of arXiv:2510.13844}
}

abstract

The formation and evolution of galaxies and other astrophysical objects have become of great interest, especially since the launch of the James Webb Space Telescope in 2021. The mass, size, and density of objects in the early universe appear to be drastically different from those predicted by the standard cosmology - the $\Lambda$CDM model. This work shows that the mass-size-density evolution is not surprising when we use the CCC+TL cosmology, which is based on the concepts of covarying coupling constants in an expanding universe and the tired light effect contributing to the observed redshift. This model is consistent with supernovae Pantheon+ data, the angular size of the cosmic dawn galaxies, BAO, CMB sound horizon, galaxy formation time scales, time dilation, galaxy rotation curves, etc., and does not have the coincidence problem. The effective radii $r_e$ of the objects are larger in the new model by $r_e \propto (1+z)^{0.93}$. Thus, the object size evolution in different studies, estimated as $r_e \propto (1+z)^s$ with $s=-1.0 \pm {0.3}$, is modified to $r_e \propto (1+z)^{s+0.93}$, the dynamical mass by $(1+z)^{0.93}$, and number density by $(1+z)^{-2.80}$. The luminosity modification increases slowly with $z$ to 1.8 at $z=20$. Thus, the stellar mass increase is modest, and the luminosity and stellar density decrease are mainly due to the larger object size in the new model. Since the aging of the universe is stretched in the new model, its temporal evolution is much slower (e.g., at $z=10$, the age is about a dex longer); stars, black holes, and galaxies do not have to form at unrealistic rates.

Figures

Figures reproduced from arXiv: 2510.13844 by the authors.

**Figure 1.** presents the angular diameter distance 𝑑𝐴 for the two models based on the model parameters obtained by fitting Pantheon+ data. We notice that except for low redshifts, 𝑑𝐴 is vastly different for the two models. And, since the physical size of an object of a measured angular size is directly proportional to 𝑑𝐴, it is also very different in the two models [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

**Figure 2.** The age comparison for the CTL and the ΛCDM models as age ratio at different redshifts 𝑧. The abscissa shows the redshift 𝑧 as well as the corresponding age of the Universe in the two models for ready reference. 3. Results Our focus in this paper is on the CTL model and comparing the results with its ΛCDM equivalent. The CTL model offers a fundamentally different cosmological perspective compared to the ΛCDM framew… view at source ↗

**Figure 3.** Comparison of the stellar mass M*, Luminosity, dynamical mass 𝑀dyn, and size R for the CTL and the ΛCDM models in the form of their ratios at different redshifts 𝑧. The abscissa shows the redshift 𝑧 as well as the corresponding age of the Universe in the two models for ready reference. Black hole mass is considered proportional to the luminosity of 𝐻𝛼 (𝐻𝛽) lines: 𝑀𝐵𝐻 ∝ 𝐿 0.55(0.56) [143-144]. Thus, black hole mass i… view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Comparison of the dynamical mass 𝑀dyn and stellar mass M* evolution in the CTL model relative to the ΛCDM models in the form of their ratios at different redshifts 𝑧. The abscis- [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Comparison of the evolution of some densities in the CTL model relative to the ΛCDM models in the form of their ratios at different redshifts 𝑧. The abscissa shows the redshift 𝑧 as well as the corresponding age of the Universe in the two models for ready reference. 4.…

**Figure 6.** Figure 6: Comparison of the evolution of the effective radius 𝑅𝑒 of galaxies with redshift 𝑧 in different studies shown in the legend [77-80, 150] and discussed in the text. Mass Evolution: As discussed above, while stellar and black hole masses depend on luminosities, the dynam…

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Works this paper leans on

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