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REVIEW 4 major objections 6 minor 1 cited by

Tsallis entropy may be the organizing principle for dark energy in a coasting universe.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-04 16:13 UTC pith:ZGKUKS55

load-bearing objection The model assumes the coasting expansion it claims to explain, and the reported constraints on δ are vacuous because the data never depend on it. the 4 major comments →

arxiv 2509.15039 v2 pith:ZGKUKS55 submitted 2025-09-18 astro-ph.CO

Holographic dark energy in a coasting cosmology

Yunliang Ren , Xiaofeng Yang , Xuwei Zhang , Shuangnan Chen , Yangjun Shi , Cheng Cheng , Xiaolong He , Hoernisa Iminniyaz This is my paper
classification astro-ph.CO PACS 95.36.+x98.80.Es
keywords dark energycoasting cosmologyholographic principleTsallis entropyTrans-Planckian Censorship CriterionType Ia supernovaebaryon acoustic oscillationscosmic chronometers
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.

The paper argues that dark energy in a uniformly expanding ('coasting') universe can be described by the holographic principle if the bounding entropy is Tsallis entropy rather than the standard Bekenstein entropy. With the Hubble horizon as the infrared cutoff, the dark energy density takes the form ρ_Λ = B H^(4−2δ), and in a coasting background (E_z = 1+z) this produces a dark-energy equation of state that evolves with redshift. The model satisfies the Trans-Planckian Censorship Conjecture, which ΛCDM fails in the far future, and it introduces just one extra free parameter (the Tsallis exponent δ). Fits to Type Ia supernovae, baryon acoustic oscillations, and cosmic chronometer data recover a value of δ consistent with theoretical expectations, and the model improves on ΛCDM by the AIC, BIC, and KIC criteria in most data combinations. If the claim holds, Tsallis entropy would be a candidate physical origin for dark energy.

Core claim

The central claim is that a flat, non-interacting dark-energy-plus-matter universe governed by Tsallis entropy S_δ = γ A^δ, with A = 4πL^2 and the Hubble horizon L = H^{-1} as the infrared cutoff, yields the holographic dark energy density ρ_Λ = B H^{4−2δ}. In a coasting universe, where the total equation of state is w_tot = −1/3 and E_z = H/H0 = 1+z, this gives Ω_Λ = (8πB/3) H0^{2−2δ}(1+z)^{2−2δ} and w_Λ = −(1+z)^{2δ−2} H0^{2δ−2}/(8πB). The paper shows that this model satisfies the TCC because the Hubble parameter never becomes constant as long as δ evolves, and that it fits SNIa+BAO+CC data with best-fit δ ≈ 1.29, giving lower AIC, BIC, and KIC values than ΛCDM in most cases. The authors r

What carries the argument

The key identity is the Tsallis holographic dark energy density ρ_Λ = B H^{4−2δ}, obtained by applying the Cohen relation between infrared and ultraviolet cutoffs with the entropy S_δ = γ A^δ. Together with the coasting condition E_z = 1+z, it determines the redshift dependence of Ω_Λ and w_Λ, and it is the object whose parameter δ is fitted to data. The same coasting relation H ∝ a^{-1} is used to verify the Trans-Planckian Censorship Criterion: wavelengths remain below the Hubble radius at all times.

Load-bearing premise

The derivation and fits assume the universe is exactly coasting (E_z = 1+z) and that δ is constant when computing Ω_Λ and w_Λ, even though TCC compliance later requires δ to become dynamical; if E_z is not exactly 1+z, or if δ genuinely evolves during the epochs probed, the reported results change.

What would settle it

Measure E(z) directly at multiple redshifts (for example with cosmic chronometers and BAO) beyond the current samples: a deviation from E(z)=1+z larger than the model's uncertainty would break the coasting premise. Alternatively, observe w(z) at high redshift: if the dark-energy equation of state does not follow the predicted monotonically increasing trend, or if late-time H(t) is seen to approach a constant, the model fails.

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

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If this is right

  • Dark energy in this model is not constant: its density scales as (1+z)^{2−2δ}, so it dilutes as the universe expands, and its equation of state w_Λ rises toward less negative values over time.
  • The universe completes the transition from matter domination to dark energy domination at higher redshift than in ΛCDM, yet continues expanding at a constant rate.
  • The model passes the Trans-Planckian Censorship Conjecture, avoiding the 'eternal acceleration' fate that ΛCDM runs into, provided δ is allowed to vary in the late future.
  • Compared with ΛCDM, the model has one extra free parameter, and information criteria (AIC, BIC, KIC) favor it for most joint data sets, with the largest improvement when BAO data are included.

Where Pith is reading between the lines

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

  • The paper derives everything with δ constant, but then proposes a dynamical δ to satisfy the TCC; a concrete equation of motion for δ(t) is absent, so the far-future behavior is a suggestion rather than a derived result.
  • If δ does vary with time, the luminosity-distance and distance-modulus formulas used in the fits would need to be recomputed, so the reported best-fit δ may not be the true one once the dynamics of δ are specified.
  • A testable signature of this specific model is the predicted monotonic rise of w_Λ with time; future measurements of the dark-energy equation of state at z ≳ 1 could confirm or exclude this.
  • The interpretation that Tsallis entropy is the fundamental origin of dark energy is not uniquely forced by the data; the same holographic construction with other non-extensive entropies or modified gravity could produce similar fits, so further discrimination tests are needed.

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

4 major / 6 minor

Summary. The paper constructs a holographic dark energy model in a coasting (w_tot = -1/3) universe by identifying the dark energy density with Tsallis entropy, rho_Lambda = B H^{4-2 delta}. It argues that coasting expansion satisfies the Trans-Planckian Censorship Criterion, derives expressions for Omega_Lambda(z) and w_Lambda(z), and then fits the parameters H0, Omega_m and delta to SNIa, BAO and cosmic-chronometer data. The paper reports a best-fit delta ~ 1.29, claims the model fits better than LambdaCDM according to AIC/BIC/KIC, and concludes that there may be a fundamental relationship between Tsallis entropy and dark energy.

Significance. If correct, the paper would offer a novel entropic origin for dark energy in a coasting cosmology and would show that such a cosmology evades the TCC constraint on eternal acceleration. The theoretical construction is clearly presented and the TCC check in Sec. II is explicit, and the observational comparison is a concrete attempt to falsify the model. However, the central observational claim is not supported by the likelihood as written, and the theoretical derivation contains an algebraic error. Because the paper's main conclusion rests on these two pillars, the current significance is low. No machine-checkable proofs or reproducible code are provided, and the MCMC setup is described only schematically.

major comments (4)
  1. [IV (Observational data), Eqs. (31)-(38)] After Eq. (31) the paper imposes E_z = 1+z, so H(z) = H0(1+z). Then the observables in Eqs. (35)-(38) reduce to mu = 5 log10[(c(1+z)/H0) ln(1+z)] + 25, D_H = c/[H0(1+z)], and D_V = (c/H0)[ln(1+z)]^{2/3}[z/(1+z)]^{1/3}. None of these quantities contains Omega_m, delta or B. The chi^2 surface in (Omega_m, delta) is therefore flat, and the posterior distributions in Fig. 2 and the best-fit values in Table I cannot be used to claim an 'optimal Tsallis parameter'. The AIC/BIC/KIC differences in Table II are likewise not evidence for the EDE model, because the extra parameters do not enter the likelihood for the fixed expansion history. The central observational claim of the paper is thus unsupported as written.
  2. [III, Eq. (23)] The second Friedmann equation is written as dot H/H^2 = -(2/3)(1 + Omega_Lambda w_Lambda). The correct coefficient for a flat FRW universe is -3/2. With Eq. (22), 1 + Omega_Lambda w_Lambda = 2/3, so one should obtain dot H/H^2 = -1 and q = 0. The printed Eq. (23) gives dot H/H^2 = -4/9 and q = -5/9, which is not coasting and contradicts the paper's own definition of q in Eq. (27). If Eq. (23) is used in Eq. (24), the solution becomes Omega_Lambda proportional to a^{-8(1-delta)/9}, not a^{2 delta - 2} as in Eq. (25). Consequently Eqs. (33)-(34), which are used for the fits, do not follow from the stated equations.
  3. [V (Conclusion), Eqs. (24)-(28)] The proposed resolution of the TCC problem is a 'dynamical Tsallis parameter' delta(t). No equation of motion for delta(t) is provided, no criterion is given for when the constant-delta assumption used in deriving Eq. (24) breaks, and no prescription is given for how a time-dependent delta would enter the distance-redshift relation used in Sec. IV. Since the derivations of Omega_Lambda(z) and w_Lambda(z) in Eqs. (25)-(26) and (33)-(34) assume delta is constant during differentiation, the TCC compliance claim for the EDE model is not established. This is a load-bearing gap, not a presentation issue.
  4. [IV, Eqs. (31)-(34) and Table I] The fitted parameter set is (H0, Omega_m, delta), but the holographic normalization B appears in Eqs. (31)-(34). Because Omega_Lambda0 = (8 pi B/3) H0^{2-2 delta}, B is necessary to predict Omega_Lambda and w_Lambda; Eq. (34) makes w_Lambda inversely proportional to B. The paper does not state whether B is fixed or free, nor its prior. Without this information, the joint constraint in Table I cannot be reproduced, and the dark-energy equation of state is not actually predicted by the model as presented.
minor comments (6)
  1. [Abstract] The phrase 'novel and simple on the evolution of the universe' is ungrammatical; consider 'novel and simple description of the evolution of the universe'.
  2. [Eq. (20)] The exponent of H in Omega_Lambda appears inconsistent with Eq. (14): with rho_Lambda = B H^{4-2 delta}, Omega_Lambda = rho_Lambda/(3 M_P^2 H^2) should be proportional to H^{2-2 delta}, not H^{2 delta - 2}. Please check the sign.
  3. [IV, text after Table I] The statement that 'delta < 2 implies that the dark energy density decreases with the increasing scale factor' is not consistent with Eq. (33), which gives Omega_Lambda proportional to a^{2 delta - 2}. For the fitted value delta ~ 1.29, Omega_Lambda increases with a. Please reconcile.
  4. [Fig. 1 caption and Table I] The figure caption uses delta = 1.2085, while Table I reports best-fit values around 1.267-1.290. Please make the quoted values consistent or explain the difference.
  5. [Conclusions] The conclusion says 'a new model with two free parameters' is constructed, but Sec. IV constrains three parameters (H0, Omega_m, delta). Clarify the relation between the two models.
  6. [Throughout] There are numerous typographical issues, e.g., 'Geraed't Hooft' for Gerard 't Hooft, 'gliding universe' for 'coasting universe', 'presenced', and 'is more constant'. A careful editing pass is needed.

Circularity Check

2 steps flagged

The EDE model's 'constraints' are vacuous: imposing E_z=1+z makes the likelihood independent of δ, so the claimed Tsallis-parameter fit and information-criterion preference do not test Tsallis entropy; TCC compliance is imported from the coasting assumption.

specific steps
  1. other [Section IV (Observational Data), Eqs. (31)-(38) and Table I]
    "In the coasting universe, E z is given as E z =1+z. Substituting this into Eq.(31), the matter density parameter can be expressed as: Ωm =1− 8πB/3 H0^{2−2δ}(1+z)^{2−2δ}. ... DH = c/H(z). DV =( dL(z)/(1+z) )^{2/3}( cz/H(z) )^{1/3}."

    With E(z)=1+z fixed, H(z)=H0(1+z); hence dL(z)=c(1+z)/H0 ln(1+z), DH=c/[H0(1+z)], DV∝1/H0, and CC data are H0(1+z). The likelihood therefore depends only on H0; δ, B, and Ωm appear only in the unobserved ΩΛ(z), wΛ(z). The MCMC 'best-fit' δ in Table I is a flat direction, not a data constraint. Calling δ≈1.29 'optimal' and 'consistent with theoretical expectations' is therefore an unconstrained parameter presented as a result. The claimed AIC/BIC/KIC preference is a test of the assumed coasting E=1+z vs ΛCDM, not of Tsallis entropy, since δ is absent from the likelihood.

  2. other [Section V (Conclusion), final paragraphs; Section III after Eq. (28)]
    "if the Tsallis parameter is treated as a constant, the Hubble parameter asymptotically approaches a constant value in the future, thereby violating the TCC. To resolve this, we propose treating the Tsallis parameter as a dynamical quantity and construct a new model with two free parameters that satisfies the TCC condition. We constrain this extended dark energy model using a combination of SNIa, CC, and three different BAO data sets..."

    The 'extended dark energy model' with dynamical δ is never defined or used. The fits in Section IV use constant δ (Table I) and impose E_z=1+z, and the TCC check in Section II is carried out for the coasting solution before δ is introduced. The conclusion that the model satisfies the TCC is therefore not a consequence of the proposed δ(t) dynamics; it is a restatement of the initial coasting assumption. The dynamical-δ proposal is a label on the already-assumed coasting model, not an independent derivation.

full rationale

The paper's central empirical claim—that the Tsallis parameter δ is constrained to δ≈1.29 and that this value 'aligns well with theoretical expectations'—is not supported by the likelihood. Section IV fixes E_z=1+z before any fit. With H=H0(1+z), the distance moduli, BAO distances, and CC Hubble points all depend only on H0; δ, B, and Ωm drop out. The MCMC therefore has two flat directions, and the reported posterior contours in Fig. 2 and Table I reflect priors or numerical artifacts, not data. The AIC/BIC/KIC comparisons are then statements about the assumed coasting expansion versus ΛCDM, not about Tsallis holographic dark energy. Separately, the promised dynamical-δ model that 'satisfies the TCC' is not implemented: the fits use constant δ and the TCC check in Section II is executed for the coasting solution. There is also an internal derivation inconsistency: with Eq. (22), Eq. (23) gives Ȟ/H² = -4/9 and q=-5/9, not q=0; the coasting result used for Eq. (25) is imported rather than derived. These issues make the paper's central claim circular in the sense that the assumed coasting E(z) is renamed as a Tsallis-entropy prediction.

Axiom & Free-Parameter Ledger

4 free parameters · 7 axioms · 1 invented entities

The model's contribution is small relative to its assumptions. It imports the holographic bound, Tsallis entropy, flatness, non-interacting fluids, and the coasting equation of state, then fits H0, Omega_m and delta. The only genuinely new degree of freedom is the power-law index delta, and it is not predicted before fitting. B is absorbed into the fitted densities. The proposed time-dependent delta is an unmodeled extra degree of freedom.

free parameters (4)
  • Tsallis parameter delta = delta ~ 1.2901 (full dataset); 1.2670 (SNIa+CC)
    The central free parameter, fitted by MCMC rather than predicted. The claim that the fitted value 'aligns well with theoretical expectations' is post hoc because theory only requires a broad range.
  • Hubble constant H0 = H0 ~ 73.68 km/s/Mpc (full dataset)
    Fitted jointly with delta and Omega_m; no uncertainties are reported in Table I.
  • Matter density parameter Omega_m = Omega_m ~ 0.2824 (full dataset)
    Fitted jointly; the holographic normalization B is derived from it via Eq. (32), so B is not independently constrained.
  • Holographic normalization B = not tabulated; Figure 1 uses B = 0.5
    Appears in rho_Lambda = B H^(4-2 delta). In the fit B is fixed by Omega_m, H0 and delta, effectively a derived fit product rather than a measured constant.
axioms (7)
  • domain assumption Cohen's holographic bound L^3 Lambda^4 <= S_BH^(3/4) is assumed as the starting point for holographic dark energy
    Taken from ref. [41]; the model's density predictions depend on this bound, not on a first-principles derivation within the paper.
  • domain assumption Tsallis entropy S_delta = gamma A^delta applies to the cosmological horizon
    Adopted from ref. [42]; non-extensive entropy is an assumption whose application to cosmological horizons is standard in the cited literature but not derived here.
  • domain assumption Flat FRW universe with no interaction between dark energy and dark matter and negligible radiation
    Assumed in Eqs. (15)-(19) and explicitly deferred as future work in Section V; the central results depend on these simplifications.
  • ad hoc to paper Coasting expansion w_tot = -1/3 and E_z = 1+z are imposed
    The model is built to reproduce coasting by substituting E_z = 1+z into Eq. (31); the TCC check in Section II assumes H proportional to a^-1 rather than testing a general expansion.
  • domain assumption The Trans-Planckian Censorship Conjecture is taken as a valid criterion
    Imported from refs. [1-3]; it acts as a sieve for cosmological models but is not derived or independently tested.
  • ad hoc to paper The Tsallis parameter can become dynamical at late times without a supplied evolution equation
    Proposed in Section V to avoid the late-time constant-H problem, but no differential equation or Lagrangian for delta(t) is provided, and the likelihood treats delta as constant.
  • ad hoc to paper delta is treated as constant during temporal differentiation in Eq. (24) and as time-dependent in Section V
    The paper does not specify when delta is constant versus dynamical; this is an unflagged internal inconsistency in the modeling assumptions.
invented entities (1)
  • Dynamical Tsallis parameter delta(t) no independent evidence
    purpose: Provides an ad hoc escape from the late-time constant Hubble parameter and TCC violation in Section V; it does not appear in the likelihood or in any equation of motion
    A time-varying delta would change the distance fits, but no evolution law or observable signature is given. It functions as an extra degree of freedom introduced to rescue the model, akin to the graviton problem.

pith-pipeline@v1.3.0-alltime-deepseek · 8620 in / 19639 out tokens · 183555 ms · 2026-08-04T16:13:44.110101+00:00 · methodology

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Cite this review

Pith. "Pith review of Holographic dark energy in a coasting cosmology." pith.science (2026). https://pith.science/paper/ZGKUKS55

@misc{pith2026250915039,
  author       = {Pith},
  title        = {Pith review of: Holographic dark energy in a coasting cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZGKUKS55}},
  note         = {Machine review of arXiv:2509.15039}
}
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read the original abstract

Coasting cosmology offers an intriguing and straightforward framework for understanding the universe. In this work, we employ the Trans-Planckian Censorship Criterion (TCC) conjecture to test the viability of the coasting cosmology and propose an entropic dark energy (EDE) model within this framework. By applying the holographic principle to constrain the dark energy density and adopting the Bekenstein entropy and Tsallis entropy as the constraining entropies of the system, we find that, in a holographic coasting cosmological framework where dark energy and dark matter evolve independently, the Tsallis entropy satisfies certain general assumptions better than the Bekenstein entropy. Thus, there may be a fundamental relationship between Tsallis entropy and dark energy. We utilize observational data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Chronometers (CC) to constrain EDE model. The optimal Tsallis parameter obtained aligns well with theoretical expectations. To evaluate the model's fit to the observed data, we calculate the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Kullback Information Criterion (KIC), and compare these metrics with those derived from $\Lambda$CDM, under which the model shows some improvement. Overall, this model provides a novel and simple on the evolution of the universe.

Figures

Figures reproduced from arXiv: 2509.15039 by Cheng cheng, Hoernisa Iminniyaz, Shuangnan Chen, Xiaofeng Yang, Xiaolong He, Xuwei Zhang, Yangjun Shi, Yunliang Ren.

Figure 1
Figure 1. Figure 1: FIG. 1: The evolution curves of the dark energy density parameter(left panel) and the equation of state [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Using di [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

discussion (0)

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Cited by 1 Pith paper

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