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REVIEW 3 major objections 4 minor 107 references

Barrow and Tsallis holographic dark energy with the Granda-Oliveros cutoff is compatible with all late-time datasets and shows a mild statistical preference over ΛCDM on the Union3 combination, though the preference hinges on GO parameters

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2026-08-03 12:30 UTC pith:TNHDQZX2

load-bearing objection The U3 'preference' over ΛCDM comes from a parameter region where the model itself breaks down; the rest of the paper is a competent but incremental MCMC update. the 3 major comments →

arxiv 2601.02567 v1 pith:TNHDQZX2 submitted 2026-01-05 gr-qc hep-th

Hints Beyond ΛCDM from Barrow and Tsallis Holographic Dark Energy with GO cutoff

G. G. Luciano , A. Paliathanasis , G. Leon , A. Sheykhi , M. Motaghi This is my paper
classification gr-qc hep-th
keywords Barrow holographic dark energyTsallis entropyGranda-Oliveros cutoffdark energymodified Friedmann equationsBayesian parameter estimationAkaike information criterionlate-time cosmology
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 establish that Barrow and Tsallis holographic dark energy with the Granda-Oliveros cutoff is a viable alternative to the cosmological constant for the late-time expansion history. The Barrow parameter Δ deforms the horizon entropy, which changes the Friedmann equation to H^(2−Δ) ∝ ρ and turns the dark energy density into a function of αH² + βḢ. Comparing the model against supernova, Hubble-parameter, and BAO data, the Bayesian analysis finds it compatible with every dataset. For the Union3 combination the non-interacting model fits modestly better than ΛCDM (ΔAIC ≈ −3.6), while for PantheonPlus the two are statistically equivalent. If the result holds, entropy-modified holographic dark energy deserves to be treated as a serious late-time alternative, with the mild Union3 hint warranting further scrutiny.

Core claim

The central claim is that replacing the Bekenstein-Hawking entropy with Barrow entropy in the thermodynamic derivation of the Friedmann equations, and taking the holographic dark energy density with the Granda-Oliveros cutoff L=(αH²+βḢ)^(−1/2), gives a late-time cosmology that fits current observations as well as ΛCDM does. The non-interacting version is statistically equivalent to ΛCDM for the PantheonPlus combination (ΔAIC = +1.73) and weakly preferred for the Union3 combination (ΔAIC = −3.63), with best-fit Barrow index Δ ≈ −0.23, corresponding to a slightly porous horizon geometry. Through the Δ → 2(ε−1) correspondence, the same conclusion transfers to Tsallis holographic dark energy. T

What carries the argument

The load-bearing mechanism is the replacement of Bekenstein-Hawking entropy by Barrow entropy S ∝ A^(1+Δ/2) in the first law of thermodynamics at the apparent horizon. That replacement changes the Friedmann equation to H^(2−Δ) = (8πG_eff/3)ρ, so a single entropic index Δ reshapes the whole background expansion. The dark energy density is then built with the Granda-Oliveros cutoff L=(αH²+βḢ)^(−1/2), giving ρ_DE = 3M_eff²(αH²+βḢ)^(1−Δ/2); α and β set how strongly the Hubble rate and its time derivative determine the horizon scale. The evolution of Ω_DE is governed by a first-order ODE whose structure depends on the combination ((Δ−2)/(3β))(Ω_DE^(2/(2−Δ)) − α), which is why α and β are strong

Load-bearing premise

The claimed statistical preference for BHDE over ΛCDM rests on letting the GO-cutoff parameters α and β float far beyond their theoretically motivated ranges; restrict them to those ranges or break the α–β degeneracy, and the preference may disappear. A secondary ambiguity: the table lists priors on A and B while results are reported for α and β, so the exact sampling setup is unclear.

What would settle it

Re-run the Union3&OHD&BAO comparison with the GO parameters fixed to the theoretically motivated ranges α ∈ [0.7, 1.0] and β ∈ [0.3, 0.9]; if ΔAIC stops being negative or shifts sign, the hint is an artifact of unconstrained parameters. Equivalently, include a high-redshift observable that fixes the α/β ratio and check whether the best-fit Δ remains around −0.23.

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

If this is right

  • If the fit is accepted, late-time acceleration does not require a cosmological constant: the entropy-corrected holographic relation with a dynamical cutoff reproduces the data.
  • Slightly negative Δ—interpreted as a porous horizon geometry rather than the sphereflake originally proposed—is favored by both datasets, and under the Tsallis map this corresponds to the sub-extensive ε < 1 regime.
  • The α–β degeneracy means that background data alone cannot pin down the GO cutoff scale; quoted limits on α and β are therefore dataset-dependent.
  • The dark-sector interaction parameter γ is only weakly bounded (upper limits around 0.09–0.13), so current observations cannot distinguish interacting from non-interacting dark sectors.

Where Pith is reading between the lines

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

  • An implication left implicit: the Union3 preference could be a prior-driven artifact. Because the best-fit α > 14.6 and β ≈ 23 sit far outside the theoretically motivated ranges α ∈ [0.7, 1.0], β ∈ [0.3, 0.9], redoing the fit with those priors is the decisive test of the 'hint beyond ΛCDM'.
  • A natural testable extension: adding a high-redshift probe sensitive to the α/β ratio (e.g., CMB or growth data) would break the degeneracy the paper documents; whether the Union3 preference survives is an open question.
  • The A/B-versus-α/β reporting wrinkle is worth resolving: priors are listed for A and B while results are reported for α and β, so re-running the sampler with direct priors on α and β would confirm the contours.
  • Because the framework is formally identical for Tsallis entropy, the constraints apply to a whole family of generalized entropies; future entropy reconstructions could target the sub-extensive regime rather than only Barrow's original sphereflake picture.

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 / 4 minor

Summary. The paper derives modified Friedmann equations from Barrow entropy, constructs Barrow Holographic Dark Energy with the Granda-Oliveros IR cutoff (and, by formal equivalence, Tsallis HDE), and studies the background evolution for non-interacting and interacting dark sectors. Using PantheonPlus and Union3 supernovae, cosmic chronometers, and DESI DR2 BAO, it runs MCMC to constrain the parameters and compares the model to ΛCDM via ΔAIC. The central claim is that the non-interacting BHDE with U3&OHD&BAO yields a weak preference over ΛCDM (ΔAIC = −3.63) with negative Barrow exponent Δ and large GO parameters α,β. The paper also plots the evolution of Ω_DE, w_DE, q, and squared sound speed for parameter values typical of the PP fit rather than the U3 best fit.

Significance. If established, the claimed preference would make generalized-entropy HDE with a local cutoff an observationally competitive alternative to ΛCDM. The thermodynamic derivation is self-contained and the analysis uses current, state-of-the-art datasets, with AIC comparison and explicit reporting of parameter degeneracies. However, as detailed below, the parameter region that drives the U3 preference is not a valid cosmological solution of the model, so the main empirical claim is currently unsupported. The paper's transparency about the α−β degeneracy and the quoted theoretical ranges is a strength.

major comments (3)
  1. [Sec. 3.1, Eq. (16); Sec. 4.3.1, Table II] The U3&OHD&BAO non-interacting best fit (Δ=−0.234, α>14.6, β=23, Ω_m0=0.462) is not a real solution over the data range. With e=2/(2−Δ)=0.895, Eq. (16) contains Ω_DE^e, which is real only for Ω_DE≥0. For this parameter set, B=(Δ−2)/(3β)≈−0.0324 and the bracket in Eq. (16) is B(Ω_DE^e−α)−1 ≤ −0.55 for all Ω_DE∈[0,0.538]. Hence dΩ_DE/dz<0 throughout, and Ω_DE crosses zero near z≈0.6, while the fitted datasets extend to z≈2.3. Beyond the crossing the model has no real evolution. The interacting fit (α=17, β=30, γ<0.127) fails identically through Eq. (22). Thus the reported χ²_min and ΔAIC=−3.63 do not correspond to a valid background, and the claimed preference over ΛCDM is not supported. The evolution plots in Sec. 4.4 use α≈1, β≈0.56 and therefore do not exhibit this problem.
  2. [Sec. 4.2, Table I, Eq. (23)] The sampling setup is ambiguous. Table I lists priors on A and B (both in [−5,0]), but the text and Table II report constraints on α and β. Equation (23) gives A=αB, B=(Δ−2)/(3β), so a uniform prior on A and B induces a strongly non-uniform, Δ-dependent prior on α and β. The reported U3 values (α>14.6, β≈23) lie near the B→0 boundary, suggesting the posterior may be prior-dominated. The authors should specify the actual sampled variables and, ideally, rerun with explicit priors on α and β or justify the A/B parameterization.
  3. [Sec. 4.3.1, paragraph on α,β ranges] The U3 best fit is far outside the theoretically motivated ranges α∈[0.7,1.0], β∈[0.3,0.9] quoted from Ref. [100]. The paper attributes this to different redshift coverage, but this is not convincing without a dedicated test, especially because the same region is unphysical by Eq. (16). A prior-restricted analysis (and, if possible, inclusion of higher-redshift data) is necessary to determine whether any statistical preference over ΛCDM survives once the GO parameters are restricted to the physically motivated domain.
minor comments (4)
  1. [Fig. 1, 2] The captions label only one model, but the panels contain both NI and I contours; also in Sec. 4.4, δ is used for Δ without being defined in the captions.
  2. [Sec. 4.2] The likelihood construction is not fully specified: covariance matrices, treatment of the supernova absolute magnitude, and BAO covariance should be stated for reproducibility.
  3. [Eq. (23)] The A and B variables are introduced but never used in the results; sticking to α,β throughout (or reporting both consistently) would remove confusion.
  4. [Sec. 4.3.2] The last line reads 'AIC−AIC_Λ =−1.67' without formatting; minor typographical issue.

Circularity Check

0 steps flagged

No significant circularity; the thermodynamic derivation is self-contained and the observational comparison is a standard in-sample fit. Minor self-citations are supportive, not load-bearing.

full rationale

The paper's derivation chain is not circular. The modified Friedmann equation (9) follows from the first law (5) with the Barrow entropy (2); the BHDE density (12) is a direct substitution of the GO cutoff (1) into (3); and the evolution equations (16) and (22) are derived from the conservation equations (13)-(14) and (19)-(20), with Ref. [74] supplying algebraic details. None of these steps assumes the posterior parameter values or the conclusion of a preference over LambdaCDM. The observational analysis is a standard Bayesian fit: parameters are estimated from the PP/U3+OHD+BAO data and compared with LambdaCDM using AIC with the 2k penalty included. The reported DeltaAIC values are in-sample goodness-of-fit differences, not independent predictions, so no fitted parameter is renamed as a prediction. Section 4.4 plots the evolution for the already fitted ranges and explicitly describes this as studying the model 'for the allowed ranges of the model parameters derived in the previous subsection using data fitting'; it is a consistency check, not a falsifiable prediction, and does not make the inference circular. The self-citations to Refs. [58,59] (negative Delta favored) and [74] (evolution/stability equations) are present but supportive: [74] is a checkable algebraic result, and [58,59] motivate negative Delta, which is an output of the fit rather than an input. The possible Omega_DE<0/unphysical branch in the U3 best-fit region, if real, is a model-consistency and domain-of-definition issue, not a circularity, since the paper's own Eq. (16) can be used to check it. Overall, there is no definitional reduction and no load-bearing self-citation chain.

Axiom & Free-Parameter Ledger

8 free parameters · 7 axioms · 0 invented entities

The model rests on a chain of assumptions from the literature: Barrow entropy, thermodynamic-gravity first law, holographic DE density, GO cutoff, and a phenomenological interaction ansatz. The only genuinely new ingredients are the datasets and the AIC comparison; the theoretical structure is inherited from [74] and earlier work.

free parameters (8)
  • H0 = 68.5±1.6 for ΛCDM; 67.9±1.7 (PP) / 66.2±1.7 (U3) for BHDE NI
    Present Hubble rate, fitted in both models with prior [60,80].
  • Ω_m0 = 0.31 for ΛCDM; 0.358^{+0.16}_{-0.02} (PP) / 0.462±0.044 (U3) for BHDE NI
    Present matter density fraction, fitted with prior [0.01,0.5].
  • r_drag = 147.5±3.5 (PP) / 148.0±3.5 (U3)
    Comoving sound horizon at baryon drag, free parameter in BAO likelihood, prior [130,160].
  • Δ (Barrow exponent) = -0.041^{+0.01}_{-0.34} (PP NI); -0.234^{+0.082}_{-0.093} (U3 NI)
    Central entropic parameter controlling the deviation from Bekenstein-Hawking entropy; fitted with prior [-1,1].
  • α (GO cutoff parameter) = 1.58^{+0.23}_{-0.55} (PP NI); >14.6 (U3 NI)
    Weight of H^2 in the GO cutoff; text reports it as free, but Table I actually lists priors on A=αB, introducing ambiguity.
  • β (GO cutoff parameter) = 1.49^{+0.49}_{-0.93} (PP NI); 23^{+10}_{-7} (U3 NI)
    Weight of H-dot in the GO cutoff; text reports it as free, with same A/B ambiguity.
  • γ (interaction coupling) = <0.086 (PP I); <0.127 (U3 I)
    Strength of dark-sector interaction Q=3γH(1+r)ρ_DE; only in interacting model, prior [0,1].
  • c^2 (HDE normalization) = 1 (fixed by hand)
    Eq. (12): C is fixed to 3M_eff^2, equivalent to c^2=1 in standard HDE; this removes a free parameter by hand.
axioms (7)
  • domain assumption The first law of thermodynamics at the apparent horizon with Barrow entropy gives the modified Friedmann equation H^{2−Δ} = (8πG_eff/3)ρ (Eq. 9).
    Section 2; this 'thermodynamic-gravity conjecture' is the foundation of the background dynamics. It is taken from [74] and not independently proven here.
  • domain assumption Barrow entropy S_Δ = (A/A0)^{1+Δ/2} is the correct entropy-area relation for the horizon.
    Eq. (2), from [55]; the model inherits it without independent evidence in this paper.
  • domain assumption Holographic dark energy density takes the Barrow-modified form ρ_DE = C L^{Δ−2} (Eq. 3).
    From [61]; combined with the GO cutoff to produce Eq. (12).
  • domain assumption The Granda-Oliveros cutoff L=(αH^2+βḢ)^{−1/2} is the relevant IR cutoff.
    Eq. (1), from [20,21]; a phenomenological choice that defines the model.
  • ad hoc to paper The dark-sector interaction Q=3γH(1+r)ρ_DE is a valid phenomenological coupling.
    Eq. (21); one of many possible Q ansätze, adopted from [83].
  • domain assumption The universe is spatially flat FLRW with apparent horizon radius r_A=1/H.
    Section 2, Eq. (4); standard modeling assumption for this analysis.
  • standard math Barrow and Tsallis entropies are equivalent under Δ→2(ε−1), so the constraints carry over to Tsallis HDE.
    Section 1 and Conclusions; used to extend the title/claims to Tsallis despite fitting only Barrow dynamics.

pith-pipeline@v1.3.0-alltime-deepseek · 16631 in / 23929 out tokens · 211276 ms · 2026-08-03T12:30:49.890461+00:00 · methodology

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read the original abstract

Barrow and Tsallis Holographic Dark Energy (HDE) are two recent extensions of the standard HDE framework, obtained by introducing generalized entropy corrections through the Barrow and Tsallis formalisms. In this work, we examine the cosmological consequences of Barrow and Tsallis HDE implemented with the Granda-Oliveros (GO) infrared (IR) cutoff. After deriving the modified Friedmann equations within the thermodynamic-gravity conjecture, we study the background evolution in both non-interacting and interacting dark sector scenarios, emphasizing the role of the entropic parameter in shaping late-time dynamics. We then confront the model with state-of-the-art observations, including PantheonPlus and Union3 Type Ia supernovae, Cosmic Chronometers and DESI DR2 BAO measurements. Using Bayesian MCMC methods, we constrain the model parameters and compare the performance of BHDE with that of $\Lambda$CDM. Our results show that BHDE is compatible with current data and can exhibit a mild statistical preference over the concordance model for certain dataset combinations. Overall, the analysis underscores the relevance of generalized entropy frameworks in late-time cosmology and identifies Barrow-Tsallis holography with the GO cutoff as a competitive alternative to $\Lambda$CDM.

Figures

Figures reproduced from arXiv: 2601.02567 by A. Paliathanasis, A. Sheykhi, G. G. Luciano, G. Leon, M. Motaghi.

Figure 1
Figure 1. Figure 1: FIG. 1: Confidence space for the posterior parameters for the non-interacting BHDE model. [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Confidence space for the best-fit parameters for the interacting BHDE model. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Evolution of Ω [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Evolution of the deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Evolution of Ω [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Evolution of the deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Evolution of [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗

discussion (0)

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