{"id":"9e233236-a537-44d9-876b-b83f6b48f280","arxiv_id":"2507.15273","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A generalized-entropy dark energy model with one fitted extra parameter returns H0 near 73 km/s/Mpc on some datasets, but the reported model-comparison statistics do not favor it over LambdaCDM.","lead":"This paper proposes a dark energy model built from a generalized entropy of the cosmic horizon and claims it can fit recent cosmological data while raising the inferred Hubble constant, potentially easing the Hubble tension. The model is an extension of earlier work by the same group, and its own model-comparison tables show the standard model is preferred.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The DESI+P18 H0=72.56 result relies on LambdaCDM-derived Planck shift parameters that are never recomputed in the entropic model; if theta* and R are re-evaluated in this cosmology, the SH0ES-independent resolution may disappear.","rationale":"The reader's weakest_assumption identifies exactly the place where the SH0ES-independent part of the central claim is least secure. The model is fitted with H0 free, so high H0 values from PantheonPlus+SH0ES are partly expected because the dataset includes the SH0ES H0 calibration. The DESI+P18 row is therefore the key independent evidence, and it depends entirely on compressed Planck shift parameters whose values were derived for LambdaCDM. The paper's own Eq. (41) shows that the modified expansion rate differs from LambdaCDM in the matter era for sigma0<1, which is precisely the fitted region. Without a re-evaluation of theta* and R, the DESI+P18 constraint cannot be regarded as valid for this model. I also note that Table III reports positive Delta AIC and Delta BIC for every dataset where the comparison is given, which contradicts the abstract's claim of phenomenological viability and further weakens the paper's interpretation; however, the compressed-Planck transferability issue is the more load-bearing problem because it targets the only independent evidence for the high H0. A focused numerical test with the corrected early-time likelihood would settle whether H0 remains high. Since the reader already rejected the paper and this concern supports that rejection, no change in verdict is needed.","tokens_in":20510,"tokens_out":8966,"duration_ms":96599,"concrete_test":"Re-run the DESI+P18 MCMC with a corrected compressed Planck likelihood: for each sampled point (H0, Omega_m0, sigma0, beta=1), numerically integrate the model's Friedmann equation including radiation to compute r_s(z_dec), z_drag, D_A(z_dec), theta*=r_s/D_A, and R=sqrt(Omega_m0)*H0*D_A(z_dec), then evaluate the P18 covariance for these predicted quantities. If the best-fit H0 drops below ~70 km/s/Mpc, or if the corrected P18 chi^2 at the old best fit increases by more than ~9, the SH0ES-independent resolution claim collapses. A faster check is to compare theta* and R predicted by Eq. (41) at z=1100 with the assumed LambdaCDM values; a shift larger than the quoted errors already signals the problem.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that the 4-parameter generalized entropy raises H0 and thereby resolves the Hubble tension. The only SH0ES-independent support for a high H0 is the DESI+P18 entry in Table II, H0=72.56+0.049-0.057. That analysis uses the compressed Planck likelihood with fixed values 100*omega_b=2.237, theta*=1.0411, and R=1.74998. These values are not model-independent summaries: theta*=r_s(z_dec)/D_A(z_dec) and R=sqrt(Omega_m0)*H0*D_A(z_dec) depend on the sound horizon and the angular diameter distance to decoupling. In the proposed model, for beta=1 and sigma0~0.87, Eq. (41) gives H(z_rec) ~ sigma0^(-1/2) H0 sqrt(Omega_m0) (1+z)^{3/2}, so the matter-era expansion rate at fixed (H0,Omega_m0) is roughly 7% higher than in LambdaCDM. The paper never recomputes r_s, z_dec, z_drag, or D_A(z_dec) from the modified Friedmann equation (15)-(18), nor does it re-evaluate the compressed Planck likelihood for the model. If the Planck constraints were applied consistently, the allowed H0 could shift back toward the LambdaCDM value, eliminating the claimed SH0ES-independent resolution. This is the load-bearing weak point: the high DESI+P18 H0 may be an artifact of using a LambdaCDM-derived likelihood for a cosmology whose expansion history differs before recombination.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper derives modified Friedmann equations from a four-parameter generalized entropy of the apparent horizon, introduces an entropic dark-energy component, and specializes to beta=1 with sigma0<1. It then fits H0, Omega_m0, and sigma0 to Cosmic Chronometer, PantheonPlus+SH0ES, DESI DR1, and compressed Planck likelihood data, reporting H0 values around 72.6-73.3 km/s/Mpc in several dataset combinations and claiming a possible resolution of the Hubble tension. It also reconstructs the deceleration parameter and dark-energy equation of state and performs an AIC/BIC comparison with LambdaCDM.","tokens_in":20814,"tokens_out":12240,"duration_ms":120715,"significance":"The formal derivation in Sections II-III is coherent, and the paper correctly notes that without the cosmological constant the entropic term alone would produce a constant deceleration parameter (Eq. 38), so the dark-energy epoch requires both Lambda and rho_g. The paper also makes use of standard public datasets and emcee/GetDist, which is good practice. However, the central claim of a Hubble-tension resolution is not supported by the analysis as presented: H0 is a fitted free parameter in every MCMC run, the theoretical matching relation Eq. (42) is never imposed, the compressed Planck likelihood is applied with shift parameters that are not model-independent, and the AIC/BIC comparison actually favors LambdaCDM for every dataset. These are load-bearing defects, not presentation issues.","major_comments":[{"comment":"The abstract and conclusion claim that the model 'provides a higher value' of H0 for certain entropic parameters, but in the data analysis H0 is a free parameter with a flat prior [40,120] in every MCMC run. The only place where H0 is related to sigma0 through the recombination-scale matching is Eq. (42), and this relation is never imposed as a constraint or used as a prediction. Moreover, Eq. (42) as printed appears inconsistent with Eq. (41): for beta != 1 the redshift scalings of H(z -> z_rec) and the LambdaCDM expression do not match, and for beta = 1 the printed relation would make H0 proportional to sigma0^2 (or sigma0^{1/2} after a straightforward derivation), which would lower H0 for sigma0 ~ 0.87 rather than raise it. Therefore the high H0 values in Table II are best-fit values of a free parameter, not predictions of the entropic model. The authors should either impose a corrected Eq. (42) in the fitting or explicitly withdraw the predictive claim.","section":"Section IV, Eq. (42), and Section V"},{"comment":"The DESI+P18 entry in Table II, H0 = 72.56 km/s/Mpc, is the only SH0ES-independent result supporting a high H0. The analysis uses the fixed compressed Planck values 100*omega_b = 2.237, theta* = 1.0411, and R = 1.74998, without recomputing the sound horizon, the drag epoch, or the angular diameter distance to decoupling in the modified model. Because theta* = r_s(z_dec)/D_A(z_dec) and R = sqrt(Omega_m0) H0 D_A(z_dec) depend on the expansion history, and because Eq. (41) changes the high-redshift expansion rate by roughly sigma0^{-1/2} ~ 1.07 at fixed (H0, Omega_m0), these LambdaCDM-derived compressed values are not transferable to the entropic cosmology. The manuscript never evaluates whether the compressed Planck likelihood is valid for Eqs. (15)-(18), so the DESI+P18 high-H0 result is unestablished as presented; the analysis must either recompute the shift parameters in this model or remove this dataset from the claimed SH0ES-independent evidence.","section":"Section V, compressed Planck likelihood"},{"comment":"The AIC/BIC comparison actually disfavors the proposed model. For all datasets DeltaAIC > 0 and DeltaBIC > 0 (CC: +2.0 and +1.5; PantheonPlus+SH0ES: +1.9 and +3.1; CC+PantheonPlus+SH0ES: +1.9 and +3.2), meaning LambdaCDM is preferred over the three-parameter entropic model in every comparison. The statement in Section V.A that for CC data the proposed model is 'strongly favored' is the opposite of what the numbers show; the positive DeltaBIC values indicate weak evidence in favor of LambdaCDM, not in favor of the model. This contradicts the abstract's claim of 'phenomenological viability' and should be corrected and discussed honestly.","section":"Section V.A, Table III"},{"comment":"The LambdaCDM entry for the PantheonPlus+SH0ES dataset in Table II reports H0 = 69.06^{+0.477}_{-0.181} km/s/Mpc. This is inconsistent with standard analyses of that dataset, which include the Cepheid distance anchors and yield H0 near 73 km/s/Mpc. This suggests that the SH0ES likelihood (or the H0 anchor) may not have been implemented as described in Section V. If the pipeline does not actually anchor H0 through the SH0ES Cepheids, then the model's H0 = 73.34 in the same row is also an artifact of the analysis setup rather than a meaningful agreement with SH0ES. The authors should clarify the exact likelihood terms used for the PantheonPlus+SH0ES dataset.","section":"Table II, PantheonPlus+SH0ES row"}],"minor_comments":[{"comment":"The model is called a 'four-parameter generalized entropy' model, but in the data analysis beta is fixed to 1 and only the combination sigma0 is constrained; the parameters alpha+, alpha-, and gamma are never varied or reported. The text should state explicitly that the fits actually test a one-parameter extension of LambdaCDM.","section":"Section V"},{"comment":"The restriction sigma0 < 1 is imposed ad hoc to keep the entropic energy density positive, and no physical prior or independent motivation is given for this range. This limitation should be acknowledged when the paper claims that a 'certain range of entropic parameters' resolves the Hubble tension.","section":"Section V"},{"comment":"The text refers to 'figure 3(a)' and 'figure 3(b)' when discussing what is labeled Figure 4 in the manuscript; the cross-references should be corrected.","section":"Section V, figure cross-references"},{"comment":"The notation changes from the entropic parameters (alpha+, alpha-, gamma, beta) to the single parameter sigma0 without a clear statement of the domain and mass dimension of sigma0 immediately after Eq. (21); please make this explicit and use the notation consistently.","section":"Section III and IV"},{"comment":"Table III would be much easier to read if it indicated explicitly which model is preferred for each criterion, because with DeltaAIC and DeltaBIC defined as model minus LambdaCDM, positive values mean LambdaCDM is preferred, which is easily misread.","section":"Section V.A, Table III"}],"recommendation":"reject","confidential_remarks":"The derivation of the modified Friedmann equations may be of some interest, but the Hubble-tension resolution claim is not supported by the current analysis. The high H0 values are fits of a free parameter, the only SH0ES-independent support relies on an unvalidated use of compressed Planck shift parameters, and the information criteria favor LambdaCDM. A revised version focused only on the formalism, or one with a complete reanalysis including recomputed CMB shift parameters and an imposed (and corrected) matching relation, would be needed before the central claim could be considered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the bottom line: the paper is a clean entropic-cosmology exercise with a claim that doesn't hold up. The derivation of the modified Friedmann equations from the 4-parameter generalized entropy is careful, and the authors are transparent about their datasets. That's the good part. The genuinely new content is the application of the 4-parameter entropy to the late universe with MCMC fits to CC, PantheonPlus+SH0ES, DESI DR1, and compressed Planck; the generalized entropy itself comes from their earlier papers. They also honestly note that without Lambda the entropic term alone cannot produce the matter-to-DE transition.\n\nThe soft spots are load-bearing. First, H0 is a free parameter in every MCMC run; Eq. (42), which would tie H0 to the entropic parameters via the recombination matching, is never imposed. So the high H0 is a best-fit output, not a prediction from the entropy. Second, Table III reports positive Delta AIC and Delta BIC for every dataset. The authors say the model is 'phenomenologically viable,' but by their own information criteria it is disfavored relative to LambdaCDM. The abstract's claim of a 'possible resolution' is not supported by their model comparison. Third, and most serious, the only SH0ES-independent evidence for a high H0 is DESI+P18 giving H0=72.56, which uses the compressed Planck likelihood with fixed theta* and R. Those shift parameters are LambdaCDM-derived values. The model's expansion history at recombination differs by about 7% for the best-fit sigma0 (see Eq. 41), so the sound horizon and drag epoch should be recomputed. The authors never do this. If the Planck constraints were applied consistently with the modified background, the allowed H0 could move back toward the LambdaCDM value and the claimed resolution could vanish. The stress-test note lands exactly there.\n\nThe formalism may be salvageable, and a careful referee could point the authors toward the missing calculation. But as a claim of Hubble-tension resolution, this paper is not ready. I would not cite it as a resolution, though I might mention it as an example of entropic-cosmology fits. A serious editor should send it to peer review, because the mathematical derivation is real and the data analysis is falsifiable, but my own verdict would be reject in its current form.","headline":"A clean entropic-cosmology derivation that overreaches: the claimed Hubble-tension resolution is a fitted parameter, and the SH0ES-independent case rests on an unvalidated Planck likelihood.","tokens_in":702,"tokens_out":954,"would_cite":false,"duration_ms":36123,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["83F05"],"pacs":["98.80.-k","95.36.+x"],"model":"deepseek-v4-flash","headline":"A four-parameter entropy of the apparent horizon is proposed as dark energy and, for a narrow parameter range, yields H0≈73 km/s/Mpc, easing the Hubble tension.","keywords":["generalized entropy","entropic cosmology","dark energy","Hubble tension","apparent horizon thermodynamics","cosmological constant","Friedmann equations","late-time cosmology"],"falsifier":"Recompute the sound horizon at decoupling and at the drag epoch using the model's modified $H(z)$ with the best-fit parameters $\\beta=1$ and $\\sigma_0\\approx 0.87$; if the resulting shift parameters $\\theta_*$ and $R$ disagree with the Planck compressed values beyond their quoted errors, the DESI+P18 value $H_0=72.56$ is not supported.","tokens_in":20207,"feed_emoji":"🌌","tokens_out":7678,"duration_ms":75635,"temperature":0.7,"pith_summary":"The paper proposes that dark energy is a consequence of the four-parameter generalized entropy of the apparent horizon in a spatially flat universe. This entropy function reduces to all previously known horizon entropies at suitable parameter values, and its modified Friedmann equations contain an entropic energy density and pressure that, together with a cosmological constant, drive the late-time matter-to-dark-energy transition. The paper's key quantitative claim is that with β=1 and σ0 near 0.83–0.93 the present Hubble parameter comes out around 72.6–73.3 km/s/Mpc, higher than the ΛCDM value, while fits to Cosmic Chronometer, supernova, DESI DR1 BAO, and compressed Planck data remain viable. That higher H0 is presented as a possible resolution of the Hubble tension.","feed_headline":"Four-parameter horizon entropy raises H0 to 73 km/s/Mpc","feed_subtitle":"The same model fits CC, supernova, BAO, and CMB data while easing the Hubble tension.","key_machinery":"The central object is the generalized entropy $S_g$, a four-parameter function of the Bekenstein-Hawking variable $S$ constructed so that Tsallis, Rényi, Barrow, Sharma-Mittal, Kaniadakis, and loop-quantum-gravity entropies are all recovered by special parameter choices. The paper feeds $S_g$ into the apparent-horizon first law $T_h\\,dS_h = -dE + W\\,dV$, which produces modified Friedmann equations; in the late-time limit the whole correction collapses to a single parameter $\\sigma_0$ that controls how much $H_0$ differs from its $\\Lambda$CDM value. The analytic form of $\\Omega_D(z)$, and hence $H(z)$, $\\omega_D(z)$, and $q(z)$, carries the comparison with data. The mechanism that raises $H_0$ is the redshift-dependent matching: requiring the model's $H(z)$ to equal $\\Lambda$CDM's near recombination while allowing $\\sigma_0<1$ at $z=0$ forces $H_0$ upward through the relation in Eq. (42).","core_discovery":"On the paper's own terms, the discovery is that the four-parameter generalized entropy $S_g = \\frac{1}{\\gamma}\\left[\\left(1+\\frac{\\alpha_+}{\\beta}S\\right)^\\beta-\\left(1+\\frac{\\alpha_-}{\\beta}S\\right)^{-\\beta}\\right]$ of the apparent horizon produces a late-universe dark-energy sector characterized by an entropic energy density $\\rho_g$ and pressure $p_g$. In the late-time limit $GH^2\\ll 1$ the deviation from $\\Lambda$CDM is governed by a single parameter $\\sigma_0$; for $\\beta=1$ and $\\sigma_0<1$ the entropic dark-energy density stays positive. Markov Chain Monte Carlo fits to CC, PantheonPlus+SH0ES, DESI DR1, and compressed Planck data return $H_0\\approx 69.9$ (CC), $\\approx 73.3$ (PantheonPlus+SH0ES), $\\approx 73.2$ (CC+PantheonPlus+SH0ES), $\\approx 72.6$ (DESI+P18), and $\\approx 73.0$ (DESI+P18+PantheonPlus+SH0ES), with $\\sigma_0$ between about 0.83 and 0.93. The $\\Lambda$CDM fits to the same data give $H_0\\approx 67.9$–$69.4$, so the model's higher $H_0$ is the advertised resolution of the tension. The scenario also reproduces the standard thermal history: a deceleration-to-acceleration transition near $z\\approx 0.5$ and a future de Sitter phase.","pith_inferences":["A decisive check the paper leaves implicit is to recompute the CMB sound horizon and drag epoch in the modified expansion; the compressed Planck shift parameters used in the DESI+P18 fit were calibrated for $\\Lambda$CDM, so a shift in $r_s$ or $r_d$ would directly change the reported $H_0=72.56$.","Because the model's Hubble function matches $\\Lambda$CDM near recombination and deviates only at low redshift, it acts as a late-time resolution; future BAO and supernova surveys at $z\\approx 1$–$2$ could distinguish the predicted $\\omega_D(z)$ from $\\Lambda$CDM.","The same four-parameter entropy can be applied to other entropy-sensitive systems, such as black-hole thermodynamics or the early universe, where the allowed $(\\beta,\\sigma_0)$ region could be constrained independently of late-time cosmology."],"forward_implications":["If the central claim holds, the same CC, PantheonPlus, DESI, and Planck data that favor $\\Lambda$CDM with $H_0\\approx 68$ also accommodate the entropic model with $H_0\\approx 73$, so the Hubble tension can be eased without changing early-universe physics.","The model predicts a smooth deceleration-to-acceleration transition near redshift $z\\approx 0.5$ and a future de Sitter phase with $\\omega_D\\to -1$, matching the standard sequence of matter and dark-energy eras.","Both the cosmological constant and the entropic energy density are needed: without $\\Lambda$ the deceleration parameter is constant and the model cannot produce the late-time accelerating transition.","With $\\beta=1$ and $\\sigma_0<1$ the entropic dark-energy density is positive throughout the evolution; the alternative branch $\\sigma_0=1$ with $\\beta\\neq 1$ gives a negative entropic energy density beyond $z\\approx 3$, which the authors set aside."],"supporting_citations":[{"why":"supplies the four-parameter generalized entropy function $S_g$ that defines the model.","marker":"[24]"},{"why":"derives the apparent-horizon thermodynamic relation that yields the modified Friedmann equations.","marker":"[2,3]"},{"why":"provides the compressed Planck shift-parameter values (100$\\omega_b$, $\\theta_*$, $R$) used in the DESI+P18 likelihood.","marker":"[113]"},{"why":"supplies the DESI DR1 BAO measurements that give the SH0ES-independent $H_0\\approx 72.56$ result.","marker":"[111]"},{"why":"provides the PantheonPlus supernova compilation used to constrain the distance modulus.","marker":"[107-109]"},{"why":"gives the local $H_0$ measurements that the model's higher $H_0$ is compared against.","marker":"[62,63]"}],"fun_headline_variants":["Four-parameter horizon entropy boosts H0 to 73 km/s/Mpc","Generalized entropy model sets H0 to 73, easing Hubble tension","Horizon entropy dark energy raises H0 to 73, fits data","Generalized entropic cosmology sets H0=73, solves Hubble tension","Entropy model lifts H0 to 73, eases tension"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the compressed Planck shift parameters, calibrated for $\\Lambda$CDM, remain valid constraints for a model whose expansion near recombination can differ from $\\Lambda$CDM through the $\\sigma_0$-dependent terms; the paper does not recompute the sound horizon or drag epoch in the modified model.","fun_headline_variants_meta":{"raw":{"variants":["Four-parameter horizon entropy boosts H0 to 73 km/s/Mpc","Generalized entropy model sets H0 to 73, easing Hubble tension","Horizon entropy dark energy raises H0 to 73, fits data","Generalized entropic cosmology sets H0=73, solves Hubble tension","Entropy model lifts H0 to 73, eases tension"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001357,"raw_usage":{"total_tokens":5561,"prompt_tokens":1056,"completion_tokens":4505,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":672,"completion_tokens_details":{"reasoning_tokens":4409}},"tokens_in":672,"tokens_out":4505,"duration_ms":35971,"temperature":1.0,"reasoning_tokens":4409,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:37:50.984398+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the sound horizon at decoupling and at the drag epoch using the model's modified $H(z)$ with the best-fit parameters $\\beta=1$ and $\\sigma_0\\approx 0.87$; if the resulting shift parameters $\\theta_*$ and $R$ disagree with the Planck compressed values beyond their quoted errors, the DESI+P18 value $H_0=72.56$ is not supported.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"provides the compressed Planck shift-parameter values (100$\\omega_b$, $\\theta_*$, $R$) used in the DESI+P18 likelihood."},{"cited_title":"Brout et al., The Astrophysical Journal 938, 110 (2022)","cited_arxiv_id":null,"evidence_quote":"supplies the DESI DR1 BAO measurements that give the SH0ES-independent $H_0\\approx 72.56$ result."}],"review_version":1}