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REVIEW 3 major objections 5 minor 79 references

Joint baryon acoustic oscillation, cosmic chronometer, and type Ia supernova data make the constant-rate expansion model R_h=ct statistically disfavored relative to the standard ΛCDM model.

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2026-08-03 14:47 UTC pith:ACCDFKMA

load-bearing objection The paper's central result holds up—ΛCDM beats R_h=ct decisively on DESI DR2 BAO + CC + Pantheon+—but the reported Bayes factor is internally inconsistent and the 'decisive evidence' framing needs correction before the paper can be trusted. the 3 major comments →

arxiv 2512.19175 v2 pith:ACCDFKMA submitted 2025-12-22 astro-ph.CO gr-qc

Joint constraints on R_h=ct cosmology from DESI DR2 BAO, CC, and SNtextit{Ia} Pantheon^+ sample

Amritansh Mehrotra , S. K. J. Pacif , A. F. Santos This is my paper
classification astro-ph.CO gr-qc
keywords R_h=ct cosmologyLambdaCDMmodel selectionbaryon acoustic oscillationscosmic chronometersType Ia supernovaeHubble constantcosmic age
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to settle whether the alternative R_h=ct cosmology, in which the universe expands at a constant rate, can compete with the standard ΛCDM model once the newest expansion-history data are combined. Using a joint likelihood built from baryon acoustic oscillations, cosmic chronometers, and 1701 type Ia supernovae, the authors compare the models on chi-square, AIC, BIC, and Bayesian evidence. They find both models fit acceptably but ΛCDM wins on every criterion: lower chi-square, lower information criteria, and a Bayes factor favoring ΛCDM. The R_h=ct model also predicts a notably older universe (about 16 Gyr) than the ΛCDM-derived age (about 13.7 Gyr), and cannot produce the deceleration-to-acceleration transition seen in the data. A sympathetic reader would take the paper as a serious, up-to-date data check that weighs against the R_h=ct hypothesis.

Core claim

The central claim is that when DESI DR2 baryon acoustic oscillations, cosmic chronometer measurements, and the Pantheon+ supernova sample are analyzed together, the R_h=ct model—defined by the condition that the gravitational horizon R_h=c/H always equals the light-travel distance c t—is statistically disfavored relative to flat ΛCDM. In the authors' analysis, ΛCDM attains a minimum chi-square of 1574.88 versus 1629.51 for R_h=ct, and the AIC and BIC differences, 52.63 and 47.24, both exceed the conventional threshold for decisive evidence. The Bayesian evidence estimate reports a log Bayes factor of -2.3 against R_h=ct, which on the standard evidence scale indicates weak-to-moderate prefere

What carries the argument

The central object is the R_h=ct condition itself: a cosmological model in which the gravitational horizon radius R_h(t)=c/H(t) equals the distance c t light has traveled since the big bang, forcing a(t) proportional to t and H(z)=H0(1+z). This single constraint removes the need for a dark energy component but fixes the deceleration parameter to q=0 at all redshifts. The paper's comparison machinery is a joint likelihood formed as the product of three dataset likelihoods (cosmic chronometers with full covariance matrix, baryon acoustic oscillation distance ratios, and type Ia supernovae), minimized for chi-square and then converted to AIC, BIC, and a log Bayes factor via nested sampling. The

Load-bearing premise

The conclusion that the data decisively favor ΛCDM assumes that the small log Bayes factor (-2.3) and the large BIC difference (47) are consistent estimates of the same model comparison, an assumption the paper does not verify.

What would settle it

Recompute the log Bayes factor from the paper's own reported BIC values using the standard large-sample correspondence lnBF ≈ ΔBIC/2; if the result is near +23.6 rather than -2.3, the paper's evidence column contradicts its 'decisive' language. Alternatively, rerun the analysis with all 31 cosmic chronometer points instead of the unexplained 15-point subset and check whether the chi-square deficit for R_h=ct shrinks or disappears.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the analysis holds, the R_h=ct model is empirically disfavored as a description of the late-time expansion history under current BAO-plus-supernova-plus-chronometer data.
  • The R_h=ct best-fit H0 of about 61 km/s/Mpc is lower than both CMB and local distance-ladder estimates, meaning the model does not resolve the Hubble tension in the direction its proponents had hoped.
  • The absence of a deceleration-to-acceleration transition in R_h=ct implies the model will continue to struggle with the redshift at which supernovae and BAO indicate accelerating expansion, regardless of future BAO precision.
  • The posterior-derived ΛCDM age of about 13.7 Gyr matching CMB-based estimates provides a consistency benchmark, while the R_h=ct age of about 16 Gyr would require a substantial revision of early structure-formation timelines.
  • AIC and BIC differences of this size support continued use of ΛCDM as the baseline expansion model in DESI-era BAO analyses.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The reported log Bayes factor (about -2.3) and the BIC difference (about 47) do not agree with the standard correspondence lnBF ≈ ΔBIC/2; this ~20-nat gap suggests the two evidence tiers are not consistent estimates of the same comparison, so a reader should not treat both as supporting the same 'decisive' conclusion.
  • The selection of only 15 of 31 available cosmic chronometer points is not explained in the paper; if the excluded points were included or reprioritized, the H(z) comparison where R_h=ct under-predicts could shift, potentially altering the gap between the models.
  • The authors' closing caveats about JWST and dynamical dark energy hint that a more flexible extension of ΛCDM—one allowing a time-varying dark energy equation of state—may outperform both models tested here, so the paper's verdict should be read as 'ΛCDM wins against R_h=ct' rather than 'ΛCDM is the final answer.'
  • A testable extension would be to rerun the comparison with the full cosmic chronometer set and with each dataset excluded in turn, isolating whether the model ranking is driven by the BAO data, the supernova data, or the chronometer selection.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper performs a joint statistical comparison of flat ΛCDM and the Rh=ct coasting model using 15 Cosmic Chronometer H(z) points, 13 DESI DR2 BAO measurements, and the Pantheon+ SNe sample with z>0.01. Both models are fitted with nested sampling, and the paper reports posteriors for H0, Ωm0, and rd, along with χ², AIC, BIC, and a Bayes factor. The central claim is that ΛCDM is preferred by all statistical criteria, with ΔAIC=52.63, ΔBIC=47.24, and lnBF=-2.3, and that this constitutes 'decisive evidence' against Rh=ct. The paper also compares H(z) and q(z) and derives posterior-propagated cosmic ages, finding t0=13.68 Gyr for ΛCDM and 16.04 Gyr for Rh=ct.

Significance. If the statistical comparison were internally consistent, this would be a useful update of Rh=ct constraints with the DESI DR2 BAO sample, and the agreement of ΛCDM parameters (Ωm=0.309±0.008, rd=147.5±8.6) with Planck provides a sanity check on the pipeline. The χ²/AIC/BIC layer is well-defined and clearly favors ΛCDM. However, the Bayesian-evidence layer is mutually inconsistent with the information-criterion layer by roughly 20 nats, so the headline 'decisive evidence' and 'all evaluated criteria' statements are not supported by the paper's own numbers. The paper also uses an unexplained 15-point subset of the 31-point CC sample, which weakens the H(z) comparison figure and the associated qualitative claim of underprediction. The core χ² result is likely robust, but the paper's advertised comprehensive model-selection conclusion requires correction.

major comments (3)
  1. [Section III, Eq. (4) and Table I] The reported lnBF=-2.3 is inconsistent with the same table's ΔBIC=47.24. Under the standard large-sample correspondence lnBF≈ΔBIC/2, the evidence should favor ΛCDM by ~23.6 nats, not 2.3. Even comparing maximum likelihoods gives ln(L_Rh/L_Λ)=-Δχ²/2=-27.3, and since evidence ≤ L_max, the reported -2.3 would require an Occam-factor ratio of order e^{25} in favor of Rh=ct, which is implausible given the reported posterior widths. This indicates a normalization or algorithmic error in the evidence calculation (the paper states dynesty is used for sampling, then says PolyChord estimates the evidence). The result that ΛCDM has lower χ² is unaffected, but Section IV's 'decisive evidence' and 'all evaluated criteria' statements are load-bearing and currently unsupported. The evidence tier must be recomputed or explicitly retracted.
  2. [Section III, Cosmic Chronometers] The paper adopts 15 of the 31 available CC measurements but provides no criterion for the selection. If the subset is not representative, the visual comparison in Fig. 2 and the associated statement that Rh=ct 'systematically underpredicts' H(z) at z≳1 are not demonstrably robust. The authors should either use all 31 points with the full Moresco covariance matrix or justify the selection and show that the 15-point subset gives the same constraints as the full sample.
  3. [Section IV, Conclusion] The phrase 'ΛCDM offers a substantially better fit and remains the preferred cosmological description according to all evaluated criteria' is contradicted by Table I, which shows lnBF=-2.3, a value the paper itself classifies as 'weak-to-moderate' on the Jeffreys scale. Even if the 2.3 is accepted, it is not 'decisive' by the paper's own quoted criterion. The abstract and conclusion should be reworded to reflect the actual strength of the Bayesian evidence or corrected after the evidence is recomputed.
minor comments (5)
  1. [Section II and III.A] Equation cross-referencing is confusing: the text says the Rh=ct Hubble parameter is 'given by equation (3)', but Eq. (3) is the CC relation H(z)=-(1/(1+z))dz/dt; the intended expression is Eq. (1), H(z)=H0(1+z). Please correct the reference.
  2. [Section III, first paragraph] The text states that the likelihood is sampled with dynesty, but after Eq. (4) states that the evidence is estimated using PolyChord. This sampler inconsistency is not just presentational; it may explain the discrepant Bayes factor. Please clarify which sampler was actually used for the reported numbers.
  3. [Abstract and title] The title in the arXiv metadata ('Joint constraints on Rh=ct cosmology from DESI DR2 BAO, CC, and SNIa Pantheon+ sample') differs from the in-paper title ('DESI DR2 Constraints on the Rh=ct Universe...'). Please harmonize.
  4. [Throughout] There are several typos and grammatical slips, e.g., 'where as' in the abstract, 'out performs' in Section V, and 'one of the principal shortcoming' in Section V. A careful proofread is needed.
  5. [Section II, Eq. (1)] The statements 'q(z)=0' and 'strictly linear expansion' are direct consequences of the ansatz a(t)∝t and are therefore not independent predictions; this is fine, but the paper should avoid implying they are separately tested outcomes.

Circularity Check

0 steps flagged

No significant circularity: the R_h=ct test is an empirical model comparison; q=0 and age=1/H0 are transparent consequences of the model ansatz, not fitted targets.

full rationale

The central claim—that ΛCDM outperforms R_h=ct on DESI DR2 BAO + CC + Pantheon+—is driven by a standard likelihood fit of both models to the same public data (Eq. 2), with model preference read from χ²_min, AIC, BIC, and lnBF. These statistics are functions of the data and model equations, not of the conclusion, so the comparison is not circular. The R_h=ct relations q(z)=0 and t0=1/H0(1+z) do follow immediately from the defining H(z)=H0(1+z) (Eqs. 1, 7, 11, 12), but the paper presents them as consequences of the model premise and does not use them as fitted observables; they are not fed back into the likelihood. The reported age 16.035 Gyr is indeed just 1/H0 for the fitted H0=61.1, and the paper explicitly calls it 'a direct consequence of its lower inferred H0', so there is no disguised independent measurement. No load-bearing argument rests on a self-citation: the Melia references define the model under test but are not used to justify the fit statistics or the preference. The only substantive issue is an internal statistical inconsistency: Table I gives lnBF=-2.3, which is hard to reconcile with ΔBIC=47.24 (expected lnBF≈ΔBIC/2≈-23.6) and with Δχ²=54.63. That is a numerical/consistency problem, not circular reasoning: the lower-χ²/AIC/BIC preference for ΛCDM is data-driven, while the 'decisive evidence' wording in Sec. IV would need a corrected evidence calculation. Because the derivation chain itself is not equivalent to its inputs, the circularity score is 0.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new entities, forces, or conserved quantities are introduced; R_h=ct is a prior-literature model [27]. The ledger is dominated by five fitted parameters (two models × H0/rd, plus Ωm in ΛCDM) and one ad hoc data-selection assumption (15 of 31 CC points). The model-selection conclusion depends on the fitted parameters, while the age and q(z) 'predictions' are analytic functions of the fits.

free parameters (5)
  • H0 (ΛCDM) = 68.3 ± 4.6 km/s/Mpc
    Fitted to the joint CC+BAO+SN likelihood; drives the ΛCDM H(z) curve, the age integral, and the model comparison.
  • Ωm0 (ΛCDM) = 0.309 ± 0.008
    Fitted; controls the shape of H(z) and the deceleration-to-acceleration transition redshift.
  • rd (ΛCDM) = 147.5 ± 8.6 Mpc
    Treated as free (uniform prior 100-300 Mpc) although Planck reports 147.09±0.26 Mpc; anchors the BAO distance ratios.
  • H0 (R_h=ct) = 61.1 ± 4.1 km/s/Mpc
    The only scale parameter of the coasting model; the reported age t0=1/H0=16.0 Gyr is an algebraic restatement of this fitted value.
  • rd (R_h=ct) = 151.4 ± 8.9 Mpc
    Free BAO anchor for R_h=ct; weakly pulled relative to the Planck value.
axioms (6)
  • standard math FLRW age-redshift relation t(z)=∫_z^∞ dz'/((1+z')H(z'))
    Invoked in Section III.B, cited to Peebles and Hogg; standard textbook cosmology.
  • domain assumption R_h=ct condition R_h=c/H=ct defines the model; hence H(z)=H0(1+z) and q=0
    The model under test (Melia & Shevchuk [27]); q=0 and linear expansion are definitional consequences, labeled 'predictions' in the abstract.
  • domain assumption L_total = L_CC × L_BAO × L_SNeIa with independent published covariances
    Joint likelihood product, Section III eq. (2); assumes no cross-dataset covariance or double counting.
  • domain assumption Cosmic-chronometer differential-age method yields model-independent H(z)
    Section III, refs [50]-[53]; validity of passive-galaxy age dating is assumed.
  • ad hoc to paper The 15-point CC subset is representative of the 31-point Moresco sample
    Section III: 'we adopt 15 Hubble parameter measurements selected from a total of 31' — no selection criterion is stated; load-bearing for the Fig. 2 H(z) comparison.
  • domain assumption Jeffreys-scale thresholds (|lnB|<1 inconclusive, >5 strong) apply to the reported lnBF
    Section III; the prose garbles the sign convention (thresholds written for positive lnB while negative is said to favor ΛCDM).

pith-pipeline@v1.3.0-alltime-deepseek · 12530 in / 23219 out tokens · 213176 ms · 2026-08-03T14:47:40.546856+00:00 · methodology

0 comments
read the original abstract

We carry out a comparative analysis of the standard $\Lambda$CDM cosmological model and the alternative $R_h=ct$ framework using recent observational data from cosmic chronometers (CC), Type Ia supernova, and baryon acoustic oscillations. The study evaluates the ability of each model to reproduce the observed expansion history of the Universe through a joint statistical assessment based on $\chi^2$ statistics, Akaike Information Criterion $(AIC)$, Bayesian Information Criterion $(BIC)$, and Bayes factor. While both models yield acceptable fits, $\Lambda$CDM consistently attains lower information-criterion values and higher likelihood, indicating a superior overall performance. An examination of the redshift evolution of the Hubble parameter $H(z)$ and the deceleration parameter $q(z)$ shows that $\Lambda$CDM naturally captures the transition from early-time deceleration to late-time acceleration, where as $R_h=ct$ predicts a strictly linear expansion. We also estimate the age of the Universe within both models, obtaining $t_0^{\Lambda CDM}= 13.676_{-0.81}^{+0.92}$Gyr and $t_0^{R_h=ct}= 16.035_{-0.98}^{+1.09}$Gyr. The posterior-derived age in the $\Lambda$CDM framework is broadly consistent with the Planck 2018 CMB result. This agreement is interpreted as a validation of the analysis pipeline and the reliability of the DESI DR2, CC, and supernova constraints, rather than as a new result for $\Lambda$CDM, and serves as a benchmark for assessing the viability of the $R_h=ct$ model. Recent JWST observations of unexpectedly mature high-redshift galaxies have renewed discussion regarding the timeline of early structure formation; although these results remain under active investigation, they underscore that fully resolving cosmic evolution may require refinements beyond the concordance paradigm.

Figures

Figures reproduced from arXiv: 2512.19175 by A. F. Santos, Amritansh Mehrotra, S. K. J. Pacif.

Figure 1
Figure 1. Figure 1: FIG. 1: The left panel of this figure shows the combined MCMC corner plot for [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Age-Redshift comparison drawn between [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The top panel presents the redshift evolution of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

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Reference graph

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