Non-flat Universe with Tsallis holographic dark energy

Alexander S. Tepliakov; Artyom V. Astashenok

REVIEW 4 major objections 4 minor 39 references

Non-flat Universe with Tsallis holographic dark energy

T0 review · 4 major / 4 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read Tsallis holographic dark energy keeps its perturbations from growing in a non-flat universe

desk verdict A plausible stability result for Tsallis holographic dark energy whose key assumption—perturbing the future event horizon rather than the fluid—is the whole ballgame, and the supplied text doesn't let me check whether they've justified it. read the letter →

arxiv 2508.16280 v1 pith:QW575UPV submitted 2025-08-22 gr-qc

Artyom V. Astashenok , Alexander S. Tepliakov This is my paper · ORCID

classification gr-qc MSC 83F05 PACS 95.36.+x98.80.Jk

keywords Tsallisholographicdarkenergyfutureeventhorizonnon-flatFLRWuniversecosmologicalperturbationsstabilityenergy–matterinteractionnon-additiveentropy

topics Dark Energy

open problems Dark Energy

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 argues that in a non-flat universe, Tsallis holographic dark energy—dark energy whose density scales with the future event horizon length raised to the power 2γ−4—does not develop the runaway density perturbations that usually plague dark-energy models. Because this dark energy is not a fluid but a boundary effect, the authors perturb the future event horizon itself rather than pressure or density. Evolving the metric and density perturbations together, they find that for realistic values of the non-additivity parameter γ, dark-energy perturbations either decay to zero or freeze at a finite value. Adding a realistic interaction between dark energy and matter preserves this behavior: perturbations can still asymptotically freeze. If correct, the result removes a standard instability objection to holographic dark energy in spatially curved universes.

What carries the argument

The key object is the future event horizon length L (with the inverse Hubble parameter as an alternative cutoff), which fixes the dark-energy density through ρ_de ∼ L^{2γ−4}. The argument's mechanism is to write δρ_de in terms of δL and to evolve δL through the perturbed Einstein equations, instead of imposing an equation of state and sound speed on the dark energy as a fluid. This 'horizon perturbation' prescription is what converts potentially divergent density perturbations into decaying or frozen solutions.

What would settle it

Compute the same coupled perturbation equations using the alternative cutoff L = 1/H (the inverse Hubble scale) instead of the future event horizon, or describe the same energy density as a fluid with a constant equation of state; if either variation produces growing modes for realistic γ, the freezing result is an artifact of the horizon-perturbation choice rather than a property of the model.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that linear perturbations of Tsallis holographic dark energy are stable in a non-flat FLRW universe. The density of this dark energy is ρ_de ∼ L^{2γ−4}, with L the future event horizon (or inverse Hubble scale) and γ close to 1. The paper treats the perturbation δρ_de as inherited from a perturbation of L, δL, and solves the coupled system of metric and horizon perturbations. For realistic γ, the solutions show dark-energy perturbations do not grow without bound: they vanish or freeze. The same holds when a realistic interaction between dark energy and matter is switched on. The paper therefore claims the model is not ruled out by perturbati

Load-bearing premise

The whole result rests on treating dark-energy perturbations as perturbations of the future event horizon rather than as density or pressure fluctuations; if horizon perturbations are not the right degree of freedom, the reported freezing does not follow.

Editorial extensions

If this is right

Tsallis holographic dark energy can be a viable dark-energy candidate in spatially curved universes without requiring a specially tuned fluid sound speed.
Matter growth in this model should differ from a fluid dark-energy model only through the decaying or frozen horizon perturbations, giving a predicted growth factor that can be compared with large-scale structure observations.
The interaction between dark energy and matter does not restore instabilities, widening the class of viable interacting holographic dark-energy models.
If dark-energy perturbations freeze rather than vanish, the dark energy may carry a small residual clustering signature rather than being perfectly smooth, which future surveys could in principle test.
The same horizon-perturbation method could be used to test the stability of other boundary-based dark-energy models.
The freezing behavior means the usual fluid notion of a dark-energy 'sound speed' is not the right description for this model; parameter constraints based on fluid dark energy may not apply.

Reading between the lines

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

The reported freezing is likely sensitive to the choice of cutoff: with L replaced by the inverse Hubble parameter, the perturbation equations may behave differently, and the paper's stability result may not carry over unchanged.
To test this model against cosmological data, one would need to implement horizon perturbations in a Boltzmann solver rather than the standard fluid dark energy module, so existing observational constraints on fluid dark energy are not directly transferable.
The approach suggests that holographic dark-energy models should be characterized by how their cutoff length responds to perturbations, not by a sound speed; this reframing could matter for other holographic and entropy-based dark-energy proposals.
A natural extension is to apply the same horizon-perturbation treatment to related models such as Barrow holographic dark energy, where the entropy-area relation differs but the boundary logic is similar.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

I could only read the abstract—the supplied full text is garbled in my copy, so this is a review of the claims, not the derivations. The claim itself is straightforward: for Tsallis holographic dark energy, if you perturb the future event horizon L rather than treating DE as a fluid, then for realistic γ the density perturbation δρ/ρ = (2γ−4)δL/L doesn't blow up; it decays or freezes, and an interaction term can freeze it too. That is a genuinely useful result for that model if the derivation holds. The paper is worth points for recognizing that holographic DE is not a local fluid and that the usual perturbative treatment may be inappropriate. That's a real conceptual point, not a dodge.

The soft spot is exactly the one the stress-test note flags. δL is a nonlocal functional of the full future metric and null geodesics. The abstract asserts that one must consider horizon perturbations, but it doesn't show—at least in the abstract—that δL obeys a closed, gauge-invariant evolution equation, or that they've included the back-reaction of δρ_DE on L. If they evolve δL as an independent scalar while ignoring its own source term, the freezing could be an artifact. I can't tell from what I have. The parameter γ being close to 1 makes the prefactor (2γ−4) small; that could be legitimate physics or a convenient tuning. The 'realistic values' phrase in the abstract would need to be backed by a clear parameter range.

For its own subfield, this is a reasonable working paper. It doesn't overturn anything, and it doesn't provide a new technology. But it addresses a real potential instability in a specific model, and the approach, if correct, removes a known objection. I'd want to see the equations before trusting it. If the full text is intact on arXiv, I'd send it to a referee—not to bury it, but to ask exactly the horizon-perturbation question. On the supplied evidence I can't sign off on the result, but I can't dismiss it either.

Referee Report

4 major / 4 minor

Summary. The paper investigates linear metric and density perturbations in a non-flat Friedmann-Lemaitre-Robertson-Walker universe filled with Tsallis holographic dark energy, with energy density rho_DE ~ L^{2γ-4}, where L is the future event horizon or inverse Hubble parameter and γ is the Tsallis non-additivity parameter close to 1. The central claim, taken from the abstract, is that because holographic dark energy is a boundary phenomenon rather than an ordinary fluid, the appropriate perturbed variable is the future-event-horizon perturbation δL rather than fluid density or pressure perturbations. For realistic parameter values the authors report that dark-energy perturbations do not grow without bound but either vanish or freeze, and that with a realistic interaction between dark energy and matter, perturbations can also freeze asymptotically. The supplied body text is corrupted and unreadable, so the underlying equations and derivations could not be independently evaluated.

Significance. If the claim is correct, the result would be significant: it would remove a standard instability concern for holographic dark energy models in non-flat cosmologies by showing that linear perturbations freeze or decay, and it would identify an important conceptual point—that perturbations of a boundary-defined energy density should be described through horizon perturbations rather than local fluid variables. The paper also offers a falsifiable prediction (no divergent dark-energy perturbations for realistic parameters), which is commendable. However, because the full text is unreadable in the provided copy and because the abstract leaves the crucial nonlocal variable δL unaccompanied by a worked derivation, the current version does not supply enough mathematical support for the claim to be checked.

major comments (4)

[Full text (post-abstract)] The supplied manuscript body is heavily corrupted (mojibake); the equations and derivations are unreadable. No equation numbers could be verified. Since the paper's central claim rests on a derivation of the perturbation equations for the future event horizon, the absence of readable mathematics is load-bearing: the reader cannot confirm that the perturbation equations are derived from the Einstein equations, that δL is gauge-invariant, or that the 'freeze' solutions are not artifacts of a truncated system. Please provide a readable version.
[Abstract (central premise)] The claim that 'one needs to consider perturbations of the future event horizon' is asserted rather than derived. δL is nonlocal, since L is an integral over future null geodesics, and is generally gauge-dependent. To make the stability conclusion load-bearing, the paper must show: (i) the perturbed Einstein equations that determine δL, including the backreaction of δρ_DE on the metric; (ii) that a gauge-invariant combination is used; and (iii) that replacing fluid perturbations by δL does not discard degrees of freedom. Without this, the vanishing/freezing behavior may be an artifact of a truncated or gauge-dependent treatment.
[Abstract (parameters)] The result is stated for 'realistic values of parameters' but no quantitative range is given in the abstract, and the body is unreadable. In particular, the parameter γ is described as 'close to 1'; since ρ_DE ∝ L^{2γ-4}, the relation between δρ_DE and δL has the prefactor 2γ-4, and the stability may hinge on whether γ < 2. The paper should state the exact parameter ranges used, show plots or tables for these values, and verify that the freezing behavior is robust to variations within the allowed range. Otherwise the 'realistic values' claim is untestable.
[Abstract (setup)] The abstract says L is 'length of event horizon or inverse Hubble parameter,' but these are physically different cutoffs and lead to different perturbation dynamics. Also, the 'realistic interaction' case is not specified. The paper must state which cutoff is used in each calculation and define the interaction term (e.g., Q = Γ ρ_m or Q = Γ(ρ_m + ρ_DE)), because both choices affect whether perturbations freeze.

minor comments (4)

[Abstract] The sentence 'perturbations also can asymptotically freeze with time' is vague; specify whether this means δ → 0, δ → constant, or something else.
[Abstract] The phrase 'Tsallis model of holographic dark energy' should include a citation to the Tsallis non-additive entropy framework and to the earlier holographic dark energy literature.
[Full text] There is an unrelated arXiv identifier 'arXiv:2508.16285v1 [cs.GT]' embedded near the beginning of the supplied text; this should be removed.
[Full text] The text contains many garbled words beyond the encoding problem; the authors should ensure a clean PDF is uploaded to arXiv before resubmission.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the freezing result is an evolution outcome, not a restatement of inputs.

full rationale

The only legible part of the supplied manuscript is the English abstract; the body text is heavily corrupted (Cyrillic mojibake), so specific equation-to-equation reductions cannot be exhibited. The abstract defines Tsallis holographic dark energy via rho_DE ~ L^(2γ-4), states that perturbations of the future event horizon are the appropriate variable, and reports that with realistic parameters the perturbations vanish or freeze. This is a claimed evolution result, not a tautology: the inputs are the horizon length, cosmological parameters, and γ; the output is the asymptotic behaviour of the perturbation. The horizon-perturbation step is an assumption and a potential gauge-sensitivity concern, but an assumption is not circularity unless the conclusion is loaded into the ansatz. No fitted parameter is renamed as a prediction, no load-bearing self-citation is visible, and no equation is quoted that reduces the result to its own definition. Under the hard rule that circularity must be exhibited by an exact quote and a specific reduction, no circular step can be identified. The score is 0, with the caveat that the illegibility of the full text prevents a deeper audit of the perturbation closure.

Assumptions & free parameters 1 free parameters · 2 assumptions · 0 invented entities

The central derivation rests on the Tsallis holographic dark energy energy-density relation and on the assumption that perturbation degrees of freedom live on the event horizon. No new entities are introduced. The only visible free parameter is γ, which is set close to 1 from observational realism.

free parameters (1)

γ (non-additivity parameter) = close to 1
The Tsallis model's energy density scales as L^(2γ-4); the abstract says γ is close to 1 and 'realistic values' are used, indicating it is taken from constraints rather than derived.

assumptions (2)

domain assumption Dark energy density is given by ρ_DE ~ L^(2γ-4), where L is the future event horizon or inverse Hubble parameter.
This is the defining relation of Tsallis holographic dark energy, adopted from prior literature.
ad hoc to paper Perturbations of holographic dark energy must be described by perturbing the future event horizon, not by fluid pressure/density perturbations.
The abstract states this explicitly: 'One needs to consider perturbations of the future event horizon.' This assumption is load-bearing for the stability result.

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Cite this review

Pith. "Pith review of Non-flat Universe with Tsallis holographic dark energy." pith.science (2026). https://pith.science/paper/QW575UPV

@misc{pith2026250816280,
  author       = {Pith},
  title        = {Pith review of: Non-flat Universe with Tsallis holographic dark energy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QW575UPV}},
  note         = {Machine review of arXiv:2508.16280}
}

abstract

We investigated evolution of metric and density perturbations for Tsallis model of holographic dark energy with energy density $\sim L^{2\gamma - 4}$, where $L$ is length of event horizon or inverse Hubble parameter and $\gamma$ is parameter of non-additivity close to $1$. Because holographic dark energy is not an ordinary cosmological fluid but a phenomena caused by boundaries of the universe, the ordinary analysis for perturbations is not suitable. One needs to consider perturbations of the future event horizon. For realistic values of parameters it was discovered that perturbations of dark energy don't grow infinitely but vanish or freeze. We also considered the case of realistic interaction between holographic dark energy and matter and showed that in this case perturbations also can asymptotically freeze with time.

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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A.G. Riess, et al., Astron. J. 116 (1998) 1009

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