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REVIEW 4 major objections 6 minor 52 references

Kaniadakis entropy lets Hubble-radius dark energy drive cosmic acceleration, a result standard holographic dark energy cannot achieve.

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Kaniadakis holographic dark energy with Hubble-radius cutoff, placed in modified Kaniadakis cosmology, can mimic a cosmological constant and accelerate the universe without interaction, though the phantom-crossing claim is inconsistent with the stated parameters.

T0 review reviewed 2026-08-04 challenge →

load-bearing objection The noninteracting acceleration result is the real novelty and it holds up, but the interacting section has a factor-of-three error and the phantom-crossing claim is not reproduced by the paper's own equations. the 4 major comments →

arxiv 2510.11569 v2 pith:SHRN76LA submitted 2025-10-13 gr-qc

Holographic dark energy in modified Kaniadakis cosmology

A. Sheykhi , A. Asvar , E. Ebrahimi This is my paper
classification gr-qc
keywords Kaniadakis entropyholographic dark energymodified Friedmann equationsHubble radius cutoffdark energy equation of statecosmological constantphantom crossingstatefinder
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 reading

This paper tries to establish that a holographic dark energy model based on Kaniadakis entropy, when placed in the modified Friedmann background that this entropy implies, can explain the observed late-time acceleration using the simplest infrared cutoff, the Hubble radius. In standard cosmology the same cutoff fails: it gives w_DE = 0 and no acceleration unless dark energy interacts with dark matter. The authors show that the Kaniadakis correction αH^{-2} changes this conclusion, yielding a noninteracting equation of state that crosses into the accelerating regime, and in a dark-energy-dominated universe producing a constant Hubble parameter and w_DE = -1, mimicking the cosmological constant. They further propose that this provides a thermodynamic origin for Λ. The paper matters because it suggests a single entropy deformation can repair a known shortcoming of holographic dark energy and naturally yield a cosmological-constant-like behavior.

Core claim

In a universe governed by Friedmann equations modified by Kaniadakis entropy, the holographic dark energy density ρ_DE = 3c^2 M_p^2 H^2 + 3α M_p^2 H^{-2} (with α ∝ K^2 and K the Kaniadakis parameter) can account for accelerated expansion with the Hubble radius as IR cutoff. For a DE-dominated universe, the modified Friedmann equation forces H = (2α/(1-c^2))^{1/4} = constant, giving a de Sitter phase with w_DE = -1. In the noninteracting two-component case, the effective equation of state w_DE = (2/Ω_DE)(c^2-Ω_DE)/(1+Ω_DE-2c^2) can be less than -1/3, unlike the standard HDE limit w_DE = 0. With interaction, the total equation of state can cross the phantom divide. The authors also show the sq

What carries the argument

The central object is the Kaniadakis-corrected holographic dark energy density combined with the modified Friedmann equations that Kaniadakis entropy generates via the thermodynamics-gravity correspondence. The Kaniadakis entropy is a one-parameter deformation of the Bekenstein-Hawking entropy, SK = (1/K) sinh(K S_BH), and its lowest-order correction S_BH + (K^2/6)S_BH^3 leads both to a modified ρ_DE and to a modified Friedmann equation of the form 3M_p^2(H^2 - αH^{-2}) = ρ_tot. The αH^{-2} term is what makes acceleration possible with the Hubble cutoff, and the same α appears in ρ_DE, creating a self-consistent structure.

Load-bearing premise

The entire result rests on importing the modified Friedmann equation 3M_p^2(H^2 - αH^{-2}) = ρ_tot, which is taken from earlier works via the thermodynamics-gravity correspondence and is not derived in this paper; with the standard Friedmann equation (α = 0) the paper's own equation of state gives w_DE = 0 and no acceleration.

What would settle it

Measure the deceleration-acceleration transition redshift z_tr from a large, homogeneous sample of supernovae and BAO over 0 < z < 1.5: the noninteracting KHDE model predicts z_tr ≈ 0.4, while ΛCDM predicts z_tr ≈ 0.64 ± 0.04. A precise determination of z_tr outside this range would rule out the model in its noninteracting form.

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

If this is right

  • Noninteracting holographic dark energy with the Hubble radius cutoff, which fails in standard cosmology, becomes viable in Kaniadakis cosmology because the correction term drives w_DE below -1/3.
  • In a dark-energy-dominated era the model evolves as pure de Sitter space with constant H and w_DE = -1, providing a concrete dynamical realization of a cosmological-constant-like phase.
  • Equating the KHDE density with the standard cosmological constant density yields Λ ∝ K, suggesting that the smallness of Λ might be tied to the smallness of the Kaniadakis deformation parameter.
  • Interaction between dark energy and dark matter allows the total equation of state to cross the phantom boundary at the present epoch, a behavior consistent with current observational hints.
  • The model predicts a deceleration-to-acceleration transition around z ≈ 0.4 in the noninteracting case, delayed compared to ΛCDM, making the transition redshift a discriminating observable.

Where Pith is reading between the lines

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

  • The cosmological-constant 'origin' claim is really a parameter relation: choosing ρ_DE = ρ_Λ fixes Λ in terms of K, c^2, and G. It does not independently predict the observed Λ unless K is independently measured; a more cautious interpretation is that KHDE offers a thermodynamically motivated parametrization of Λ.
  • Because the αH^{-2} correction grows at late times (as H decreases), the Kaniadakis term naturally becomes important in the recent epoch, which may offer a mechanism for late-time acceleration that strengthens with cosmic expansion.
  • The model's viability hinges on the modified Friedmann background; if future observations or theoretical considerations restore the standard background, the noninteracting acceleration result evaporates and the model reverts to the standard HDE failure.
  • The negative squared sound speed suggests the model is perturbatively unstable; this could be tested with growth-of-structure data, which would either constrain the interaction parameter or rule out the model as a physical dark energy candidate.
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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 proposes a Kaniadakis holographic dark energy (KHDE) model with the Hubble radius as IR cutoff, set in the modified Friedmann cosmology that arises from Kaniadakis entropy via the thermodynamics-gravity correspondence. The main claims are: (i) in a DE-dominated universe the model yields a constant Hubble parameter and w_DE = -1, thereby 'mimicking' the cosmological constant and offering a possible origin for Λ; (ii) in the noninteracting two-component case the model can drive present acceleration for the Hubble-radius cutoff, in contrast to standard HDE where w_DE = 0; (iii) in the interacting case the total equation of state can cross the phantom line; (iv) the model is unstable according to the squared sound speed and is distinguishable from ΛCDM via statefinder diagnostics. The noninteracting derivation (Eqs. 27-39) is internally consistent and does show w_DE < -1/3 for c² < 0.654 at Ω_DE0 = 0.7. However, the interacting section contains algebraic inconsistencies: the announced interaction term Q = 3b²H(1+r)ρ_DE does not lead to Eqs. (43)-(44), and the quoted equations do not reproduce the claimed phantom crossing with the stated parameters.

Significance. If the noninteracting acceleration result is correct, it is a noteworthy result: it shows that a modified entropy/gravity framework can rescue the Hubble-radius HDE model without invoking an interaction or a more complicated cutoff. The analytical derivations are explicit and reproducible, which is a strength. However, the significance is tempered by two factors. First, the entire new phenomenology depends on the modified Friedmann equation (11), which is imported from refs. [35,36] and not derived here; if the standard Friedmann equation were used, the paper's own Eq. (27) gives w_DE = 0 and no acceleration. Second, the 'theoretical origin of Λ' claim in Eq. (22) merely relates Λ to the free parameters K and c², providing no independent determination of those parameters; it is a reparametrization rather than an explanation. The interacting-sector errors further undermine the phantom-crossing and stability conclusions. The paper does not provide observational constraints or numerical fits, but as a theoretical study it could be of interest to the holographic-dark-energy community if the algebraic issues are resolved.

major comments (4)
  1. [§II.C, Eqs. (40)-(47)] The interaction term is defined as Q = 3b²H(1+r)ρ_DE after Eq. (41), but the subsequent equations do not follow from this Q. Repeating the derivation with the announced Q gives w_DE = 2(c² - Ω_DE - b²/2)/[Ω_DE(1+Ω_DE-2c²)], not Eq. (43) with b²/6; and Ω'_DE = 6(Ω_DE - c²)(1 - Ω_DE - b²)/(1+Ω_DE-2c²), not Eq. (44). Even if one assumes the coupling should be Q = b²H(1+r)ρ_DE, Eq. (44) still has a coefficient 3 where the consistent derivation yields 2. Thus the interacting evolution equations are internally inconsistent, and this error propagates into q, w_tot, v_s², and the statefinder.
  2. [§II.C, Fig. 3] The text states that 'w_DE crosses the phantom divide at the present time' and that for all b² choices w_DE lies in the phantom regime at the present epoch. However, evaluating the paper's own Eq. (43) with the stated parameters Ω_DE0 = 0.7, c² = 0.5 and b² = 0, 0.03, 0.06 gives w_DE ≈ -0.82, -0.84, -0.86 at z = 0, all above -1. The claimed phantom crossing is therefore not reproduced by the quoted equations. The figures appear to have been generated with a different expression, and the text and equations need to be reconciled.
  3. [Eq. (22) and Abstract] The claim that KHDE 'implies that the theoretical origin of the cosmological constant, Λ, may be understood through KHDE' is an overinterpretation. Equation (22) expresses Λ in terms of the free parameters K and c². Since K and c² are not determined by the model, this is a reparametrization of Λ, not a derivation of its value or origin. The authors should either soften the claim or provide an independent argument that fixes K and c².
  4. [Eq. (11) and §II.B] The central acceleration result depends entirely on the modified Friedmann equation 3M_p²(H² - αH^{-2}) = ρ_m + ρ_DE, which is taken from refs. [35,36] without derivation. If α = 0, the paper's own Eq. (27) gives w_DE = 0 and no acceleration. The novelty of the result is therefore conditional on accepting the thermodynamics-gravity correspondence that produces this particular background. The authors should state this dependence more prominently and discuss the robustness of their conclusions against alternative modifications of the Friedmann equations.
minor comments (6)
  1. [After Eq. (41)] The sentence 'Negative sign of Q indicates a transfer of energy from DE to DM' is reversed. With Q > 0, Eq. (40) shows DE loses energy and Eq. (41) shows DM gains energy; the opposite holds for Q < 0.
  2. [General] Figures are referenced as 'Fig.II C' instead of proper numbers (e.g., Fig. 1, Fig. 2, etc.). This is likely a LaTeX artifact and should be fixed.
  3. [Abstract] The introductory sentence has a grammatical error: 'any modification to the entropy expression not only change' should be 'changes'.
  4. [§II.C, last paragraph] The sentence 'Note that these results are in agreement with other researches on KHDE, that appeared after the present work' is self-referential and inappropriate for a research paper. It should be rephrased to compare with existing literature without asserting temporal precedence.
  5. [Eq. (33)] The expression for w_tot is unnecessarily complicated and can be simplified by using Ω_DE and H/H0 directly. The notation ρ_cr0 in the denominators is confusing; suggest rewriting in terms of dimensionless densities.
  6. [§III.A] The squared sound speed analysis in Eq. (51) inherits the errors of the interacting-sector equations. After correcting w_DE and Ω_DE', the stability conclusion (v_s² < 0) should be re-examined.

Circularity Check

1 steps flagged

Only the Λ-origin claim reduces to a free-parameter redefinition; the central acceleration derivation is independent.

specific steps
  1. renaming known result [Section II.A, Eqs. (19)-(22)]
    "Equating the energy density of KHDE with energy density of cosmological constant Λ, namely ρDE = ρΛ = Λ/(8πG) for the case of DE dominated universe, one can easily find Λ = 3πK/2G (1+c^2)/√(1-c^2). ... This may provide a theoretical origin for the cosmological constant through thermodynamic arguments."

    The claim that KHDE explains the origin of Λ is obtained by imposing ρDE = ρΛ and solving for Λ in terms of the free parameters K and c^2. Since K is not fixed by any independent mechanism, Λ=Λ(K,c^2) is a reparametrization of the model's constant energy density, not an independent prediction. Any model with a constant energy density can be relabeled Λ; the 'origin' statement therefore reduces by construction to the equality that was inserted as input.

full rationale

The paper's central results (wDE=-1 in a DE-dominated universe and acceleration for noninteracting KHDE with L=H^{-1}) are algebraic consequences of the defining equations. Given the modified Friedmann equation (11) and the KHDE density (8), Eqs. (18)-(21) and (27) follow by substitution and conservation; they do not assume the conclusions. The modified background is imported from the authors' earlier papers [35,36], but this is a reliance on a published derivation of the background equations rather than a self-citation that itself contains the present target result; the cited equations are externally testable and are not restatements of the KHDE acceleration claim. The interacting-sector phantom-crossing statement is not reproduced by the authors' own Eq. (43) with the quoted parameters, but that is an algebraic/consistency problem, not circular reasoning. The only circular-adjacent step is the cosmological-constant 'origin' relation of Eq. (22), which is a free-parameter redefinition as described above; the core derivation is otherwise self-contained.

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The model's new phenomenology comes almost entirely from the assumed modified Friedmann equations (imported from the authors' earlier papers) and the assumed αH^-4 correction in ΩDE; the remaining parameters (c², K, b², ΩDE0) are free or tuned, so the paper adds model-building machinery rather than a parameter-free prediction.

free parameters (4)
  • c² = 0.5 (adopted in figures; c²<0.654 is required for acceleration at ΩDE0=0.7)
    Holographic constant in ρDE=3c²Mp²H²+3αMp²H^-2; controls wDE and the acceleration condition Eq. (28).
  • K (or α) = K=0.1 used in figures; consistency with ΩDE0-c² and observed Λ would require K to be extremely small (~10^-60–10^-120 de
    Kaniadakis parameter entering α=K²π²/(2G²); controls the magnitude of the correction and the effective Λ in Eq. (22); not independently measured.
  • b² = 0, 0.03, 0.06 (chosen for plots)
    Coupling constant in the dark-sector interaction term Q; free parameter of the interaction ansatz.
  • ΩDE0 = 0.7
    Present-day dark-energy density parameter, adopted from observations as the initial condition for the ODEs; not predicted by the model.
axioms (5)
  • domain assumption Modified Friedmann equations (11)–(12) derived from Kaniadakis entropy via thermodynamics-gravity correspondence
    Imported from refs [35,36]; the αH^-2 term in the first Friedmann equation is the source of the new phenomenology.
  • domain assumption Kaniadakis entropy expansion S_K = S_BH + (K²/6) S_BH³ + O(K⁴) for K≪1
    Used to obtain the KHDE energy density in Eq. (7); assumes K is small.
  • domain assumption Holographic bound ρL⁴ ≤ S with IR cutoff L=H^{-1}
    Defines the KHDE energy density in Eqs. (7)–(8).
  • domain assumption FRW flat metric and standard total conservation equation (13)
    Background geometry and conservation assumed throughout.
  • ad hoc to paper Interaction Q = 3b²H(1+r)ρDE
    Phenomenological interaction ansatz from [43]; the derived equations are actually consistent with a version lacking the factor 3, so the stated form is internally mismatched.

reviewed 2026-08-04 · how reviews work

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Cite this review

Pith. "Pith review of Holographic dark energy in modified Kaniadakis cosmology." pith.science (2026). https://pith.science/paper/SHRN76LA

@misc{pith2026251011569,
  author       = {Pith},
  title        = {Pith review of: Holographic dark energy in modified Kaniadakis cosmology},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SHRN76LA}},
  note         = {Machine review of arXiv:2510.11569}
}
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abstract

It is well-known that any modification to the entropy expression not only change the energy density of the holographic dark energy, but also modifies the cosmological field equations through thermodynamics-gravity correspondence. Here we propose a Kaniadakis holographic dark energy (KHDE) in the background of the modified Kaniadakis cosmology by incorporating the effects of Kaniadakis entropy into the Friedmann equations. We choose the Hubble radius, $L=H^{-1}$, as system's IR cutoff and determine the cosmological implications of this model. We first consider a dark energy (DE) dominated universe and reveal that this model mimics the cosmological constant with $w_{DE}=-1$. This implies that the theoretical origin of the cosmological constant, $\Lambda$, may be understood through KHDE in the context of Kaniadakis cosmology. Remarkably, we observe that in the absence of interaction between DE and dark matter (DM), and in contrast to HDE in standard cosmology, our model can explain the current acceleration of the cosmic expansion for the Hubble radius as IR cutoff. When the interaction between DE and DM is taken into account, we see that the total equation of state parameter (EoS), $w_{tot}=p_{tot}/\rho_{tot}$ can cross the phantom line at the present time. We also analyze the squared speed of sound, $v_s^2$, for this model and find out that $(v_s^2<0)$ for interacting KHDE. Investigating the statefinder, confirms the distinction between KHDE and $\Lambda$CDM model. It is seen that the statefinder diagram move away from the point of $\left\lbrace r,s\right\rbrace= \left\lbrace 1,0\right\rbrace$ with increasing the interaction parameter.

Figures

Figures reproduced from arXiv: 2510.11569 by A. Asvar, A. Sheykhi, E. Ebrahimi.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗

discussion (0)

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Reference graph

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.