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arxiv: 2601.02408 · v1 · submitted 2026-01-02 · ⚛️ physics.gen-ph

A Combined Barrow Entropy and QCD Ghost Mechanism for Late-Time Cosmic Acceleration

Aziza Altaibayeva , Ulbossyn Ualikhanova , Zhanar Umurzakhova , Surajit Chattopadhyay This is my paper

Pith reviewed 2026-05-16 18:40 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords Barrow entropyQCD ghostdark energycosmic accelerationholographic dark energyFriedmann equationsquintessence
0
0 comments X

The pith

The BH-QCDGDE model merges Barrow entropy corrections with QCD ghost effects to produce a viable late-time cosmic acceleration.

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

This paper constructs a unified dark-energy density by combining Barrow-deformed entropy corrections with low-energy QCD vacuum effects inside a single generalized holographic expression. Inserted into the Friedmann equations for a flat FLRW universe, the density produces a smooth transition from matter-dominated deceleration to late-time acceleration. The resulting equation-of-state parameter stays above the phantom divide, and an equivalent scalar-field reconstruction exhibits quintessence-like behavior. Thermodynamic consistency is verified by satisfaction of the generalized second law at the apparent horizon, while classical stability is checked through the squared speed of sound.

Core claim

The central claim is that the BH--QCDGDE framework, defined by a generalized holographic dark-energy density that incorporates both Barrow-deformed entropy corrections and low-energy QCD vacuum effects, supplies a consistent background evolution for late-time acceleration in a spatially flat FLRW universe, admits a quintessence-like scalar-field description, satisfies the generalized second law throughout the parameter space, and yields stable regimes under the squared-speed-of-sound criterion.

What carries the argument

The generalized holographic dark-energy density that folds Barrow-deformed entropy corrections together with QCD ghost vacuum contributions and is substituted directly into the Friedmann equations.

Load-bearing premise

The combined Barrow-QCD generalized holographic dark-energy density can be inserted straight into the Friedmann equations to control the background expansion without extra fine-tuning or internal inconsistencies.

What would settle it

A clear measurement that the dark-energy equation-of-state parameter has crossed below -1 at low redshifts would contradict the model's no-phantom-crossing behavior.

Figures

Figures reproduced from arXiv: 2601.02408 by Aziza Altaibayeva, Surajit Chattopadhyay, Ulbossyn Ualikhanova, Zhanar Umurzakhova.

Figure 1
Figure 1. Figure 1: Three-dimensional evolution of the total equation-of-state parameter [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Three-dimensional evolution of the deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Three-dimensional evolution of the total equation-of-state parameter [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Three-dimensional evolution of the deceleration parameter [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Scalar-field reconstruction of the BH–QCDGDE model. The left panel shows [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Scalar-field reconstruction for the power-law scale factor [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Reconstructed scalar potential V (ϕ) as a function of the scalar field ϕ and the model parameters. Top left: variation with the holographic parameter α in the observationally viable range α ≤ 0.2, for fixed Ωm0 = 0.3, Ωr0 = 8 × 10−5 , β = 0.12, and ∆B = 0.1. Top right: variation with the QCD ghost parameter β in the range 0.05 ≤ β ≤ 0.2, keeping Ωm0 = 0.3, Ωr0 = 8 × 10−5 , α = 0.01, and ∆B = 0.1 fixed. Bot… view at source ↗
Figure 8
Figure 8. Figure 8: Three–dimensional evolution of the normalized total entropy production rate [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Three-dimensional behavior of the squared speed of sound [PITH_FULL_IMAGE:figures/full_fig_p022_9.png] view at source ↗
read the original abstract

We investigate a unified dark-energy scenario based on the combined effects of Barrow entropy corrections and the QCD ghost mechanism, referred to as the BH--QCDGDE model. The dark-energy density is constructed in a generalized holographic form that incorporates both Barrow-deformed entropy corrections and low-energy QCD vacuum effects within a single framework. The cosmological dynamics are analyzed in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker background. The model exhibits a smooth transition from a decelerated matter-dominated era to a late-time accelerated phase without crossing the phantom divide, indicating a viable background evolution. An equivalent scalar-field description of the effective dark-energy sector is reconstructed and shown to admit a quintessence-like behavior. The thermodynamic viability is examined by testing the generalized second law at the apparent horizon, which is found to be satisfied throughout the parameter space. The classical stability of the model is further investigated through the squared speed of sound, revealing the role of model parameters in shaping stable cosmological regimes. Overall, the BH--QCDGDE framework provides a consistent and physically viable description of late-time cosmic acceleration.

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 proposes the BH--QCDGDE model, a unified dark-energy scenario in which a generalized holographic density combines Barrow entropy corrections with QCD ghost contributions. This density is inserted into the Friedmann equations for a flat FLRW background to analyze the expansion history. The work reports a smooth transition from matter-dominated deceleration to late-time acceleration without phantom crossing, reconstructs an equivalent quintessence scalar field, verifies satisfaction of the generalized second law at the apparent horizon, and examines classical stability via the squared sound speed, concluding that the framework provides a consistent description of late-time cosmic acceleration.

Significance. If the central derivations are confirmed, the model supplies a thermodynamically motivated alternative to standard holographic dark energy that incorporates both entropy deformation and QCD vacuum effects within a single effective fluid. The explicit quintessence reconstruction and parameter-dependent stability analysis add concrete content beyond purely phenomenological fits, potentially offering falsifiable predictions for the equation-of-state evolution and sound-speed behavior that could be tested against supernova, BAO, or CMB data.

major comments (2)
  1. [cosmological dynamics and equation-of-state derivation] The central construction assumes that the combined Barrow+QCD density can be substituted directly into the Friedmann and acceleration equations while preserving the standard continuity equation for the effective fluid. No explicit verification is provided that ρ̇_DE + 3H(ρ_DE + p_DE) = 0 holds identically once both corrections are included; if the Barrow deformation modifies the holographic bound while the QCD term is added separately, extra source terms may appear. This must be shown algebraically in the section deriving w_DE (or the equivalent pressure) before the background evolution and stability claims can be accepted.
  2. [parameter space and stability analysis] The model parameters that control the transition redshift, the avoidance of phantom crossing, and the sign of c_s² are introduced to produce the desired late-time acceleration and stability regimes. The manuscript should clarify whether these parameters are fixed by independent physical considerations (e.g., QCD scale or Barrow exponent bounds) or are adjusted post-hoc to fit the observed acceleration; otherwise the claim of a “consistent and physically viable description” risks being circular.
minor comments (2)
  1. [thermodynamic viability section] The abstract states that the generalized second law is satisfied “throughout the parameter space,” yet the text should specify the exact range of the Barrow exponent and QCD coefficient for which this holds, together with the numerical method used to integrate the horizon entropy.
  2. [model definition] Notation for the effective dark-energy density should be introduced once and used consistently; the current text alternates between “generalized holographic form” and “BH–QCDGDE density” without a single defining equation early in the manuscript.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major comment below and will revise the manuscript to strengthen the presentation.

read point-by-point responses

  1. Referee: The central construction assumes that the combined Barrow+QCD density can be substituted directly into the Friedmann and acceleration equations while preserving the standard continuity equation for the effective fluid. No explicit verification is provided that ρ̇_DE + 3H(ρ_DE + p_DE) = 0 holds identically once both corrections are included; if the Barrow deformation modifies the holographic bound while the QCD term is added separately, extra source terms may appear. This must be shown algebraically in the section deriving w_DE (or the equivalent pressure) before the background evolution and stability claims can be accepted.

    Authors: We agree that an explicit algebraic verification is required for clarity. The combined density is defined as a single effective fluid within the generalized holographic setup, so the continuity equation is expected to hold by construction once p_DE is obtained from the acceleration equation. In the revised manuscript we will insert a dedicated paragraph (or short subsection) immediately after the expression for w_DE that explicitly computes ρ̇_DE from the Friedmann equation, substitutes the derived p_DE, and demonstrates that ρ̇_DE + 3H(ρ_DE + p_DE) = 0 is satisfied identically with no residual source terms. This will remove any ambiguity before the background evolution and stability sections. revision: yes

  2. Referee: The model parameters that control the transition redshift, the avoidance of phantom crossing, and the sign of c_s² are introduced to produce the desired late-time acceleration and stability regimes. The manuscript should clarify whether these parameters are fixed by independent physical considerations (e.g., QCD scale or Barrow exponent bounds) or are adjusted post-hoc to fit the observed acceleration; otherwise the claim of a “consistent and physically viable description” risks being circular.

    Authors: We thank the referee for highlighting the need for clearer physical grounding. The Barrow exponent Δ is bounded by 0 < Δ ≤ 1 from the original thermodynamic derivation of Barrow entropy. The QCD ghost scale is fixed by the known QCD vacuum energy scale (∼100 MeV). The remaining holographic prefactor is constrained by requiring that the model reproduces the observed transition redshift z_t ≈ 0.6–0.8 and remains quintessence-like (w > −1). In the revised version we will add a dedicated paragraph in the parameter discussion section that (i) states the independent bounds on Δ and the QCD scale, (ii) explains how the holographic constant is chosen within the narrow window that satisfies these observational anchors without phantom crossing, and (iii) notes that the stability regimes for c_s² follow directly from these physically motivated ranges rather than being tuned after the fact. This will eliminate any appearance of circularity while preserving the model’s predictive content. revision: partial

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines a generalized holographic dark-energy density by combining Barrow entropy corrections with the QCD ghost term, substitutes this expression directly into the standard flat FLRW Friedmann equations, and then solves the resulting background evolution. The late-time acceleration emerges from the functional form of the combined density for chosen parameter ranges, but this is not a reduction by construction because the density is an independent ansatz whose parameters are not fitted to the acceleration itself within the paper; instead, the model is tested for thermodynamic consistency (generalized second law at the apparent horizon) and classical stability (squared sound speed) as separate checks. No self-citation load-bearing steps, uniqueness theorems, or fitted-input predictions are present in the abstract or described chain. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on a standard flat FLRW geometry plus an ad-hoc generalized holographic density that merges two previously separate corrections; several free parameters are required to tune the transition and stability.

free parameters (1)
  • Barrow and QCDGDE model parameters
    Parameters that control the strength of entropy corrections and ghost contributions are introduced to produce the observed acceleration and stable regimes.
axioms (2)
  • domain assumption Spatially flat FLRW metric governs the background cosmology
    Standard assumption invoked for the Friedmann equations and apparent-horizon thermodynamics.
  • ad hoc to paper Generalized holographic dark-energy density incorporates both Barrow and QCD ghost terms
    The combined density form is postulated within the model rather than derived from first principles.

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Reference graph

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