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arxiv: 2604.21490 · v2 · pith:TEKNKYGSnew · submitted 2026-04-23 · 🌌 astro-ph.CO · gr-qc

Impact of the Infrared Cutoff on Structure Formation in Tsallis Holographic Dark Energy

Biswajit Das This is my paper

Pith reviewed 2026-05-08 14:19 UTC · model grok-4.3

classification 🌌 astro-ph.CO gr-qc
keywords cutoffgrowthhorizonmodelsdarkenergyholographicstructure
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The pith

THDE models with future event horizon IR cutoff match observed cosmic structure growth rates comparably to ΛCDM, whereas particle horizon versions do not.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Cosmologists use holographic dark energy to explain the universe's accelerated expansion by linking it to information on the cosmic horizon. The Tsallis version modifies the entropy formula with a parameter. The infrared cutoff defines the horizon scale used in the energy density formula. This work compares two common choices: the particle horizon, which is the distance light has traveled from the Big Bang, and the future event horizon, which is the distance light will travel in the future. They solve for how small density fluctuations in matter grow over time, calculating the growth factor and the observable f sigma 8 at different redshifts. When compared to measurements from galaxy surveys, the future horizon models align well with data for certain values of the Tsallis parameter, sometimes matching or exceeding the standard Lambda CDM model. Particle horizon models, however, predict too little or incorrect growth and disagree with observations. This sensitivity shows that the cutoff choice is vital for the model's success in describing structure formation.

Core claim

We find that the growth history is highly sensitive to the choice of IR cutoff. Models based on the future event horizon are consistent with observational data and can provide a fit comparable to, or slightly better than, the ΛCDM model for suitable values of the Tsallis parameter δ. In contrast, models constructed using the particle horizon generally fail to reproduce the observed growth of structure.

Load-bearing premise

The assumption that the Tsallis parameter δ can be freely adjusted to fit the data without additional theoretical constraints, and that the linear perturbation analysis accurately captures the relevant physics without higher-order effects.

read the original abstract

We investigate the viability of Tsallis holographic dark energy (THDE) models, focusing on the role of the infrared (IR) cutoff in the growth of cosmic structures. Considering two commonly used choices of the cutoff, the particle horizon and the future event horizon, we analyze the evolution of linear matter perturbations and compute the growth factor, growth rate, and the observable $f\sigma_8(z)$. These predictions are compared with observational data from redshift-space distortion measurements. We find that the growth history is highly sensitive to the choice of IR cutoff. Models based on the future event horizon are consistent with observational data and can provide a fit comparable to, or slightly better than, the $\Lambda$CDM model for suitable values of the Tsallis parameter $\delta$. In contrast, models constructed using the particle horizon generally fail to reproduce the observed growth of structure. These results demonstrate that the viability of THDE models depends crucially on the choice of IR cutoff and highlight the importance of structure formation as a stringent test of generalized holographic dark energy scenarios.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates Tsallis holographic dark energy (THDE) models with particle-horizon and future-event-horizon infrared cutoffs. It derives the background evolution, solves for linear matter perturbations to obtain the growth factor D(a), growth rate f(z), and the observable fσ8(z), then compares these predictions to redshift-space distortion data. The central claim is that future-event-horizon THDE models reproduce the observed growth history for suitable values of the Tsallis parameter δ (comparable to or slightly better than ΛCDM), whereas particle-horizon models fail to do so, demonstrating strong sensitivity to the choice of IR cutoff.

Significance. If the perturbation treatment is shown to be complete, the work provides a concrete demonstration that structure-formation observables can discriminate among holographic dark-energy prescriptions that are degenerate at the background level. Explicit fσ8 comparisons and the clear contrast between the two cutoffs constitute a useful addition to the literature on generalized holographic models.

major comments (2)
  1. [§4] §4 (linear perturbation analysis): the growth equation is written in the standard form δ_m'' + (2 + H'/H)δ_m' − (3/2)Ω_m δ_m = 0 with no source term from δρ_de. For the future-event-horizon cutoff L = ∫_t^∞ dt'/a(t'), which is non-local, a perturbation δL induces a non-zero δρ_de that must enter both the Poisson and continuity equations. The manuscript does not state whether this contribution is included or set to zero; if the latter, the reported growth histories for the future-horizon case rest on an unverified closure assumption that is known to be questionable for non-local holographic cutoffs.
  2. [§5 and §6] Parameter choice and fitting procedure (throughout §5 and §6): δ is described as taking 'suitable values' that produce acceptable fits to fσ8 data. Because the growth predictions are then tuned rather than predicted a priori, the claim that future-horizon models are 'consistent with observational data' carries a circularity burden. The manuscript should either (i) derive theoretical priors on δ or (ii) present the fσ8 curves for a fixed, untuned range of δ and quantify the tension with data without post-hoc adjustment.
minor comments (2)
  1. [Abstract and §5] The abstract and §5 state that the future-horizon models provide 'a fit comparable to, or slightly better than, the ΛCDM model' but supply no quantitative measures (χ², AIC, or posterior odds) or the specific data sets and covariance matrices employed.
  2. [§4] Numerical implementation details (integration method for the non-local cutoff, step-size convergence, initial conditions for the perturbation ODE) are not provided, making independent reproduction difficult.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments have helped us clarify important aspects of the perturbation treatment and parameter presentation. We address each major comment below and have made revisions to improve the manuscript.

read point-by-point responses

  1. Referee: [§4] §4 (linear perturbation analysis): the growth equation is written in the standard form δ_m'' + (2 + H'/H)δ_m' − (3/2)Ω_m δ_m = 0 with no source term from δρ_de. For the future-event-horizon cutoff L = ∫_t^∞ dt'/a(t'), which is non-local, a perturbation δL induces a non-zero δρ_de that must enter both the Poisson and continuity equations. The manuscript does not state whether this contribution is included or set to zero; if the latter, the reported growth histories for the future-horizon case rest on an unverified closure assumption that is known to be questionable for non-local holographic cutoffs.

    Authors: We appreciate the referee highlighting this subtlety. The manuscript employs the standard sub-horizon matter growth equation, which sets the δρ_de source term to zero. This is a standard approximation adopted in numerous holographic dark energy studies to isolate the matter sector. We have revised §4 to state this assumption explicitly and added a brief discussion of its limitations for non-local cutoffs, noting that a full treatment would require deriving δL and its back-reaction on the Poisson equation. Such an extension lies beyond the present scope but does not alter the central finding that the two IR cutoffs produce qualitatively different growth histories. The revision clarifies the closure without changing the reported numerical results. revision: yes

  2. Referee: [§5 and §6] Parameter choice and fitting procedure (throughout §5 and §6): δ is described as taking 'suitable values' that produce acceptable fits to fσ8 data. Because the growth predictions are then tuned rather than predicted a priori, the claim that future-horizon models are 'consistent with observational data' carries a circularity burden. The manuscript should either (i) derive theoretical priors on δ or (ii) present the fσ8 curves for a fixed, untuned range of δ and quantify the tension with data without post-hoc adjustment.

    Authors: We agree that the original wording risked implying post-hoc tuning. The values of δ were first constrained by requiring the background expansion to remain consistent with Planck and supernova data; growth predictions then follow. To remove any ambiguity, we have revised §§5–6 to display fσ8(z) for a fixed, untuned grid (δ = 1.0, 1.5, 2.0, 2.5) that spans the range commonly considered in the Tsallis literature. For each fixed δ we report the χ² against the RSD compilation and the corresponding tension relative to ΛCDM. The future-horizon models with δ ≈ 1.5–2.0 remain compatible with the data at a level comparable to ΛCDM, while the particle-horizon models are excluded across the entire grid. We have also added references to existing bounds on δ from non-extensive thermodynamics, although a first-principles prior remains an open theoretical question. revision: partial

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model introduces the Tsallis generalization but relies on standard cosmological perturbation theory and fitting of δ.

free parameters (1)
  • Tsallis parameter δ
    Chosen to provide good fit to fσ8(z) data for the future horizon model.
axioms (2)
  • domain assumption The Tsallis holographic dark energy density is given by ρ_DE = B L^{2δ-4} where L is IR cutoff
    This is the defining relation for THDE models.
  • standard math Linear theory for matter density perturbations with DE affecting via Hubble and equation of state
    Standard in cosmology for growth factor calculation.

pith-pipeline@v0.9.0 · 5477 in / 1427 out tokens · 48464 ms · 2026-05-08T14:19:08.087355+00:00 · methodology

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