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REVIEW 3 major objections 5 minor 8 cited by

Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Barrow and Tsallis holographic dark energy fit the latest BAO data but are disfavored by the Akaike Information Criterion, with H0 essentially unchanged.

desk verdict The DESI DR2 constraints on Barrow/Tsallis HDE rest on an ODE branch that generically violates the defining future-event-horizon relation; the paper needs a boundary-condition fix before its central numbers can be trusted. read the letter →

arxiv 2506.03019 v1 pith:HEMSKXHE submitted 2025-06-03 gr-qc hep-th

Giuseppe Gaetano Luciano , Andronikos Paliathanasis , Emmanuel N. Saridakis This is my paper
classification gr-qchep-th MSC 83F0583B05 PACS 98.80.-k95.36.+x
keywords BarrowentropyTsallisholographicdarkenergyfutureeventhorizonDESIDR2BAOconstraintsHubbletensionAkaikeinformationcriterion
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 asks whether two generalized holographic dark energy scenarios, Barrow and Tsallis, survive the newest baryon acoustic oscillation data from DESI DR2 when combined with supernova distances and cosmic-chronometer Hubble measurements. It finds that both models fit the combined data well, with the deformation exponent near its standard zero value and the recovered $H_0$ close to the $\Lambda$CDM value. The decisive step is a model-comparison test: the Akaike Information Criterion penalizes the extra parameter enough that both models score about 4 points worse than $\Lambda$CDM, meaning the data do not favor them. The conclusion is conditional on the future-event-horizon cutoff used for the holographic bound, and the paper stresses that the entropy models themselves are not ruled out in other frameworks.

What carries the argument

The load-bearing object is the generalized entropy-area relation $S=(A/A_0)^{\delta}$, which replaces the Bekenstein-Hawking area law and turns the holographic bound into the dark-energy density $\rho_{\rm DE}=C R_h^{\Delta-2}$, where $R_h$ is the future event horizon and $\Delta$ is the Barrow deformation parameter. Substituting this density into the Friedmann and continuity equations yields a first-order differential equation for the dark-energy fraction $\Omega_{\rm DE}(a)$ whose evolution is governed by $\Delta$ and a dimensionless constant $Q$ that absorbs the unknown amplitude $C$. The analysis integrates this equation numerically and fits it to the data; the same equations cover the Tsallis case through the identification $\delta\to 1+\Delta/2$. The Akaike Information Criterion then decides whether the extra parameters buy enough improvement in $\chi^2$ to be preferred.

What would settle it

Re-run the fits with a prior that allows negative $\Delta$ values (down to $-1$, as quantum-fractal arguments permit) and a wider $Q$ range; if the best-fit $\Delta$ moves negative and the AIC difference relative to $\Lambda$CDM drops below 2, the paper's claim that the models are disfavored would not survive that prior choice.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that Barrow and Tsallis holographic dark energy, defined through the power-law entropy $S=(A/A_0)^{\delta}$ with $\delta=1+\Delta/2$ for Barrow and the future event horizon as the infrared cutoff, are observationally viable but statistically disfavored. The DESI DR2 BAO data, combined with supernova and cosmic-chronometer data, bound the Barrow exponent to $\Delta<0.54$ (SN+BAO) and $\Delta<0.47$ (SN+OHD+BAO) at 1$\sigma$, with $\Delta=0$ inside the contours; the Tsallis exponent $\delta=1+\Delta/2$ therefore sits near the standard area-law value. The best-fit $H_0$ is $72.7^{+3.9}_{-3.9}$ for SN+BAO but $68.6^{+1.3}_{-3.3}$ for the full combination, essentially the $\Lambda$CDM value, so the $H_0$ tension is not alleviated. Relative to $\Lambda$CDM, the $\chi^2$ difference is $+0.2$ to $+0.7$ while the AIC difference is $+4.2$ to $+4.7$, which the paper reads as a clear preference for the concordance model. It also emphasizes that this is a statement about the holographic-dark-energy application, not about Barrow or Tsallis entropy as such.

Load-bearing premise

The analysis assumes that the entropy-area deformation exponent carries over directly into the dark-energy density as a power law and that the unknown amplitude $C$ can be absorbed into an independent parameter $Q$ with prior $Q\in[-2,5]$, along with $\Delta\in[0,1)$; if the true prior should allow negative $\Delta$ or a different $Q$ range, the reported constraints and AIC verdict could change.

Editorial extensions

If this is right

  • Both Barrow and Tsallis holographic dark energy with a future-event-horizon cutoff remain viable fits to the SN+OHD+DESI DR2 BAO data, with $\Delta\chi^2$ no worse than about $+0.7$ compared with $\Lambda$CDM.
  • The AIC penalty of roughly $+4$ means that adding the entropy-deformation parameter does not pay for itself; current observations prefer $\Lambda$CDM.
  • The full-data $H_0$ posterior lands at about $68.6$ km s$^{-1}$ Mpc$^{-1}$, so these models do not relieve the Hubble tension.
  • The 1$\sigma$ upper bounds on $\Delta$ ($<0.54$ for SN+BAO, $<0.47$ for SN+OHD+BAO) keep the entropy close to the standard area law, with $\Delta=0$ inside the contours.
  • The sign of the favored deformation differs from applications of the same entropies in gravity-thermodynamics modifications, where negative $\Delta$ was preferred; here the contours extend toward positive $\Delta$.

Reading between the lines

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

  • The paper's 'not favored' verdict is tied to treating $Q$ as a free parameter; a microphysical derivation of the amplitude $C$ that fixed $Q$ would remove one degree of freedom and could shrink or reverse the AIC penalty.
  • Because both entropy models produce the same background equations, future data can only distinguish Barrow from Tsallis through theoretical priors on the entropy exponent, not through the expansion history alone.
  • A natural next test is structure growth: the paper leaves it to future work, but a perturbative analysis using CMB lensing or $S_8$ data could change the viability verdict more directly than additional BAO points at the same redshifts.
  • Since the best-fit $\Delta$ is near zero, the practical content of the constraint is that future-event-horizon holographic dark energy is nearly degenerate with $\Lambda$CDM at the background level; distinguishing them will require probes of the dark-energy equation of state at late times.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper constrains Barrow and Tsallis holographic dark energy models, which coincide cosmologically under the identification δ = 1 + Δ/2, using Pantheon+ supernovae, cosmic-chronometer Hubble data, and DESI DR2 BAO measurements. The authors solve the evolution equation for the dark-energy density fraction, Eq. (17), with the initial condition Ω_DE(z→0)=1−Ω_m0, and run MCMC with Cobaya to constrain H0, Ω_m0, Δ, Q, and r_drag. They report that both models are consistent with the combined datasets while being disfavored relative to ΛCDM by ΔAIC ≈ +4, and that the fitted H0 remains close to the ΛCDM value, so the H0 tension is not alleviated. They also find a posterior tendency toward positive Δ, which they contrast with the preference for negative Δ found in their companion gravity-thermodynamics analysis.

Significance. If the reported constraints are reliable, the paper provides a timely DESI DR2 test of two widely studied entropy-based dark-energy models and a straightforward AIC comparison with ΛCDM, which is exactly the kind of evidence the community needs when assessing these alternatives. The use of external datasets and an independent benchmark is a strength, as is the explicit statement of the models' limitations. However, the central numerical implementation must be validated before the results can be accepted, because the paper does not demonstrate that the solutions of the differential equation it uses actually satisfy the defining future-event-horizon relation.

major comments (3)
  1. [III, Eq. (17) and the initial condition] The model is defined by the nonlocal relation (16) with ρ_DE = C R_h^{Δ−2}. Equation (17) is obtained by differentiating (16), and the two equations are not equivalent. The paper solves (17) as an initial-value problem with Ω_DE(z→0)=1−Ω_m0, which imposes no condition on the solution as x→∞. For Δ>0, the generic solution of the linearized equation for u=1−Ω_DE decays as u∝e^{-(1+Δ)x}, whereas the branch that actually satisfies the future-event-horizon relation (16) decays as u∝e^{-3x}; only the latter yields a finite R_h with a de Sitter future. The paper reports no check that the numerical solution satisfies (16) at any redshift. Consequently, the H(z) used in the likelihood and the resulting posteriors for Δ, Q, and H0 are not generally those of the claimed Barrow/Tsallis HDE model. The authors should impose the boundary condition at infinity (for example, by a shooting method or by solving the integral equation directly) or demonstrate explicitly that their initial-value-problem solution satisfies (16) to numerical precision.
  2. [III, prior on Δ] The prior Δ∈[0,1) restricts the analysis to non-negative Barrow exponents even though the Introduction cites theoretical arguments for negative Δ (Refs. [52,53]) and the companion paper [78] finds negative values favored in a different framework. With this one-sided prior, the statement that 'the contours spread to positive values' and the contrast with [78] are partly predetermined by the prior rather than by the data. The authors should either extend the prior to allow negative Δ, in line with the cited literature, or present a sensitivity test with a two-sided prior, and should frame the conclusion as a constraint under the stated prior rather than as an intrinsic tendency of the model.
  3. [III, numerical implementation and reproducibility] The paper does not report the ΛCDM best-fit parameters or the absolute χ² values, only differences, and it does not specify the exact BAO observables (e.g., D_M/r_d, D_H/r_d, D_V/r_d) and redshift bins from DESI DR2 that enter the likelihood. Without these details, the information-criterion comparison and the claimed consistency with DESI DR2 cannot be fully reproduced by an independent analysis. This is secondary to the boundary-condition issue but is nonetheless important for the paper's conclusions to be verifiable.
minor comments (5)
  1. [Table I] There is a typo in the table caption: 'Talbe I' should be 'Table I'.
  2. [Throughout] The word 'scenaria' is used repeatedly; the standard English plural is 'scenarios'.
  3. [III, prior on Q] The prior Q∈[−2,5] deserves more discussion, because Q is defined through Eq. (18) in terms of C, H0, and Ω_m0; a uniform prior on Q does not correspond to a uniform prior on C, and the sensitivity of the posteriors to this choice should be tested.
  4. [III, H0 conclusion] The statement that 'the H0 tension cannot be alleviated' is based on H0=68.6^{+1.3}_{−3.3} for the SN+OHD+BAO combination; the quoted error is large and the value is consistent with both Planck and SH0ES within 2σ, so a more precise formulation would be that the model does not significantly shift H0 relative to ΛCDM.
  5. [Figure 1] In Figure 1, the contours for Δ are cut off at the prior boundary Δ=0, so the lower part of the posterior is not visible; the authors should either show the full prior range or explicitly report the one-sided limit in the text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the constraints are driven by external SN, OHD, and DESI DR2 BAO data with an independent ΛCDM AIC benchmark; self-citations provide model origin and comparison but are not load-bearing.

full rationale

The paper's central results — parameter constraints on Δ and Q, the best-fit H0, and the AIC comparison — are obtained by MCMC likelihood analysis against external datasets (Pantheon+ SNIa, cosmic-chronometer OHD, and DESI DR2 BAO), not by feeding fitted values back into the target claims. The ΛCDM benchmark is fitted to the same data, and the AIC difference is a standard penalized-likelihood comparison using the number of model parameters. The Barrow/Tsallis HDE equations, including the energy density (2), the event-horizon relation (5), and the evolution equation (17), are explicitly derived in the paper from the entropy-area relation (1) and the future-event-horizon definition (4); the model is not merely imported via self-citation. Citations to the authors' earlier works [38,43,78,108,109] supply the model's origin and a comparison framework (gravity-thermodynamics Barrow/Tsallis cosmology), but none of these citations carries the evidential weight of the present constraints. The possible issue that solving the differentiated ODE (17) with a present-day initial condition may not enforce the integral relation (16) is an internal-consistency or correctness concern, not circularity: no predicted quantity is equivalent by construction to the fitted inputs, and no fitted parameter is renamed as a prediction. Hence the derivation is self-contained against external benchmarks and the circularity score is zero.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The model parameters (Delta, delta, Q) come from prior literature [19,38,43] and are fitted, not newly postulated entities. No new particles, forces, or dimensions are introduced.

free parameters (5)
  • H0 = 68.6+1.3-3.3 (SN+OHD+BAO); 72.7+3.9-3.9 (SN+BAO)
    The Hubble constant is a free parameter with prior [65,80] km/s/Mpc, fitted to the combined datasets.
  • Omega_m0 = 0.316+0.020-0.023 (SN+OHD+BAO); 0.312+0.026-0.026 (SN+BAO)
    The present-day matter density parameter is a free parameter with prior [0.2,0.4].
  • Delta = <0.471 (SN+OHD+BAO); <0.542 (SN+BAO)
    The Barrow exponent is a free parameter with prior [0,1), controlling the entropy deformation.
  • Q = 1.57+0.68-0.88 (SN+OHD+BAO); 1.51+0.55-1.10 (SN+BAO)
    The dimensionless parameter defined in Eq (18) absorbs the constant C; it is fitted with prior [-2,5].
  • r_drag
    The sound horizon at the drag epoch is fitted as part of the BAO likelihood.
assumptions (5)
  • standard math The standard Friedmann equations and FRW metric describe the background cosmology.
    Section II, Eqs (3)-(7), assume a spatially flat, homogeneous and isotropic universe with pressureless matter.
  • domain assumption The holographic dark energy density takes the form rho_DE = C R_h^(Delta-2) with the future event horizon as the IR cutoff.
    Section II, Eq (5), adopted from [38,43], assumes the modified entropy power law translates directly into the energy density.
  • domain assumption The future event horizon is the correct IR cutoff for holographic dark energy.
    Section II, Eq (4), described as 'the most widely accepted definition in the literature'.
  • ad hoc to paper The Barrow exponent is restricted to Delta in [0,1) and the Tsallis identification delta = 1 + Delta/2 is applied.
    Section III priors impose Delta in [0,1) even though the introduction notes arguments for negative values and [78] favored negative Delta.
  • ad hoc to paper The initial condition Omega_DE(z=0) = 1 - Omega_m0 fixes today's dark energy density from the matter density.
    Section III MCMC setup uses this boundary condition, so the model does not predict Omega_m0 but fits it.

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Cite this review

Pith. "Pith review of Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data." pith.science (2026). https://pith.science/paper/HEMSKXHE

@misc{pith2026250603019,
  author       = {Pith},
  title        = {Pith review of: Constraints on Barrow and Tsallis Holographic Dark Energy from DESI DR2 BAO data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HEMSKXHE}},
  note         = {Machine review of arXiv:2506.03019}
}
abstract

Barrow and Tsallis Holographic Dark Energy (HDE) are two recently proposed extensions of the standard HDE framework, incorporating generalized corrections to horizon entropy through the use of Barrow and Tsallis entropies. Tsallis entropy arises from non-extensive statistical phenomena which account for long-range correlations and deviations from additivity, while Barrow entropy emerges from quantum-gravitational effects on the horizon geometry, associated with fractal modifications and deformations. At the cosmological level, both scenarios lead to the same equations, nevertheless the involved parameters obey different theoretical bounds. In this work, we use observational data from Supernova Type Ia (SNIa), Cosmic Chronometers (CC) and Baryonic acoustic oscillations (BAO), including the recently released DESI DR2 dataset, to place constraints on both scenaria. We show that both can be in agreement with observations, although they cannot alleviate the $H_0$ tension. However, applying information criteria we deduce that both of them are not favoured comparing to $\Lambda$CDM concordance cosmological paradigm.

Figures

Figures reproduced from arXiv: 2506.03019 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

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Forward citations

Cited by 8 Pith papers

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