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arxiv: 2602.12077 · v2 · pith:5YFS66RXnew · submitted 2026-02-12 · 🌀 gr-qc · astro-ph.CO· hep-ph· hep-th

Cosmographic Connection Between Cosmological And Planck Scales: The Barrow-Tsallis Entropy

Yu. L. Bolotin , V.V. Yanovsky , D. A. Yerokhin This is my paper

Pith reviewed 2026-05-21 13:19 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.COhep-phhep-th
keywords Barrow-Tsallis entropyquantum foamcosmographic parametersnonextensive entropycosmological modelsPlanck scalefractional derivativeshorizon entropy
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The pith

Barrow-Tsallis entropy establishes exact link between Planck-scale quantum foam and cosmological nonextensive effects

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

The authors use the Barrow-Tsallis entropy to connect the microscopic structure of quantum foam with macroscopic nonextensive effects in the universe's evolution. They apply a general method for parameter determination in cosmological models to derive an exact relationship between the Barrow parameter for quantum gravity effects and the Tsallis parameter for nonextensivity. This means that measurements of the universe's expansion can inform quantum gravity models directly. The relations are exact, with uncertainty coming only from current knowledge of cosmographic parameters. The same approach is used to check if fractional derivatives can describe the late-time accelerated expansion.

Core claim

The Barrow-Tsallis entropy, which accounts for quantum gravitational effects through a deformed horizon area and nonextensive effects through a power-law generalization, leads to an exact relationship between its two parameters when applied to cosmological models. This relationship is obtained by the general parameter-finding method and depends on the values of cosmographic parameters such as the deceleration and jerk parameters. The resulting connections between microscopic and macroscopic scales are therefore precise within the limits of observational uncertainty in those parameters.

What carries the argument

The Barrow-Tsallis entropy form that combines a fractal dimension parameter for the quantum horizon with a nonextensivity parameter for long-range interactions

If this is right

  • The exact parameter relationship allows cosmographic data to constrain quantum gravity effects at the Planck scale.
  • Uncertainty in the link between scales is determined solely by the precision of current cosmographic observations.
  • The method can assess the viability of fractional derivative descriptions for the late universe evolution.
  • Direct translation of cosmological observations into microscopic structure parameters becomes possible.

Where Pith is reading between the lines

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

  • If the relation holds, it suggests that nonextensive statistics at cosmic scales are directly determined by the fractal nature of the quantum horizon.
  • Future improvements in measuring the Hubble parameter evolution could tighten bounds on quantum foam structure.
  • The approach might extend to other modified entropy models to find similar scale connections.
  • Independent tests could come from comparing the derived parameters with those from black hole thermodynamics or other quantum gravity approaches.

Load-bearing premise

The Barrow-Tsallis entropy correctly describes both the effects of quantum gravity on the cosmological horizon and the nonextensive character of gravitational long-range forces.

What would settle it

A future high-precision determination of cosmographic parameters, such as the deceleration parameter q0, that results in values for the Barrow and Tsallis parameters inconsistent with their expected physical ranges from quantum gravity or statistical mechanics.

Figures

Figures reproduced from arXiv: 2602.12077 by D. A. Yerokhin, V.V. Yanovsky, Yu. L. Bolotin.

Figure 1
Figure 1. Figure 1: FIG. 1: Dependence of parameter [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Barrow parameter [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Relation [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The allowable region for the jerk parameter [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

One of the fundamental challenges of quantum gravity is to understand how the microscopic degrees of freedom of the cosmological horizon shape the evolution of the Universe. One possible approach to this problem is based on the Barrow--Tsallis entropy. This entropy accounts for both quantum gravitational effects and the nonextensive effects inherent in any long-range interaction. Using a general method we developed for finding the parameters of cosmological models, we discovered a relationship between the parameter describing the microscopic structure of quantum foam and the parameter associated with macroscopic nonextensive effects. We also used our method for finding the parameters of cosmological models to evaluate the feasibility of using fractional derivatives to describe the late evolution of the Universe. The resulting relationships are exact. Therefore, the uncertainty in the relationship between the model parameters depends only on the current uncertainty in the values of the cosmographic parameters.

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 / 1 minor

Summary. The manuscript claims that a general method developed by the authors for determining parameters of cosmological models yields an exact relationship between the Barrow parameter (encoding quantum-foam microstructure on the horizon) and the Tsallis parameter (encoding nonextensive effects from long-range interactions). The uncertainty in this relation is asserted to originate solely from cosmographic parameters. The same method is applied to assess the feasibility of fractional derivatives for late-time cosmic evolution.

Significance. If the derivations establish that the general method introduces no additional scale-dependent assumptions or biases beyond the cosmographic inputs, and if the exactness of the Barrow-Tsallis relation survives independent checks, the result would provide a concrete link between Planck-scale quantum-gravity features and observable cosmology. Explicit credit is due for attempting a parameter-free-style connection once the cosmographic inputs are fixed.

major comments (2)
  1. [Abstract and parameter-relation section] Abstract and the section presenting the parameter relation: the assertion that the relationships are exact and that uncertainty depends only on cosmographic parameters is load-bearing, yet the text supplies no derivation showing that the authors' general method maps the entropy form to cosmology without injecting extra assumptions or model-specific corrections; this must be supplied explicitly with intermediate steps.
  2. [Section describing the general method] The section on the general method: because the claimed exact relation is obtained by feeding cosmographic parameters (themselves extracted from observations) into the self-developed procedure, a concrete demonstration is required that the procedure does not correlate with or amplify the same observational uncertainties, otherwise the circularity concern remains unresolved.
minor comments (1)
  1. [Introduction] Notation for the Barrow and Tsallis parameters should be introduced with explicit reference to their standard definitions in the literature to prevent ambiguity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight important points about the presentation of our general method and the claimed exactness of the Barrow-Tsallis parameter relation. We address each major comment below and have revised the manuscript to strengthen the exposition while preserving the original results.

read point-by-point responses

  1. Referee: [Abstract and parameter-relation section] Abstract and the section presenting the parameter relation: the assertion that the relationships are exact and that uncertainty depends only on cosmographic parameters is load-bearing, yet the text supplies no derivation showing that the authors' general method maps the entropy form to cosmology without injecting extra assumptions or model-specific corrections; this must be supplied explicitly with intermediate steps.

    Authors: We agree that the intermediate steps of the mapping were insufficiently explicit. The general method we previously developed extracts model parameters directly from the cosmographic series expansion of the scale factor without reference to a specific entropy form or additional scale-dependent assumptions. In the revised manuscript we have inserted a new subsection that walks through the substitution of the Barrow-Tsallis entropy into the Friedmann equation, followed by term-by-term matching to the cosmographic coefficients. This shows that the only inputs are the observed cosmographic parameters and that no model-specific corrections are introduced. The exact algebraic relation between the Barrow and Tsallis parameters follows immediately from this matching. revision: yes

  2. Referee: [Section describing the general method] The section on the general method: because the claimed exact relation is obtained by feeding cosmographic parameters (themselves extracted from observations) into the self-developed procedure, a concrete demonstration is required that the procedure does not correlate with or amplify the same observational uncertainties, otherwise the circularity concern remains unresolved.

    Authors: The general method is a purely algebraic inversion of the cosmographic Taylor series and does not involve any statistical fitting or re-derivation of the cosmographic parameters themselves; it therefore cannot amplify or correlate uncertainties beyond those already present in the input values. To make this explicit we have added a short paragraph and an accompanying error-propagation formula that expresses the variance of the derived Barrow-Tsallis relation solely in terms of the published uncertainties on the cosmographic coefficients. No new observational data or model-dependent priors enter the procedure. revision: yes

Circularity Check

2 steps flagged

Exact Barrow-Tsallis relation derived via authors' prior general method, with cosmographic inputs treated as sole uncertainty source

specific steps
  1. fitted input called prediction [Abstract]
    "Using a general method we developed for finding the parameters of cosmological models, we discovered a relationship between the parameter describing the microscopic structure of quantum foam and the parameter associated with macroscopic nonextensive effects. ... The resulting relationships are exact. Therefore, the uncertainty in the relationship between the model parameters depends only on the current uncertainty in the values of the cosmographic parameters."

    The exact relation is presented as a discovery, yet it is obtained by feeding observed cosmographic parameters into the authors' previously developed parameter-extraction procedure. The assertion that uncertainty resides solely in those cosmographic values implies the Barrow-Tsallis link is a direct algebraic consequence of the mapping, not an independent theoretical prediction.

  2. self citation load bearing [Abstract]
    "Using a general method we developed for finding the parameters of cosmological models, we discovered a relationship..."

    The load-bearing step that converts the Barrow-Tsallis entropy into an exact inter-parameter relation rests on the authors' own general method. No external theorem, machine-checked derivation, or independent data constraint is cited to establish that this method preserves exactness or introduces no additional model-specific bias.

full rationale

The paper's central result—an exact relation between the Barrow quantum-foam parameter and the Tsallis nonextensivity parameter—is obtained by applying a 'general method we developed' to cosmographic data. This method is invoked both to discover the relation and to evaluate fractional derivatives, yet no independent cross-check or external derivation is supplied. Because the claimed exactness follows directly from the mapping performed by the authors' own procedure, and the uncertainty is asserted to reside only in the input cosmographic parameters, the derivation reduces to a re-expression of fitted quantities within the self-developed framework. This constitutes fitted-input-called-prediction circularity at the level of the headline claim, while the remainder of the manuscript (entropy definitions, horizon thermodynamics) remains non-circular.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete; the central relationship rests on the domain assumption that Barrow-Tsallis entropy simultaneously encodes quantum-gravity and nonextensive effects, with cosmographic parameters serving as the sole source of uncertainty.

free parameters (2)
  • Barrow quantum-foam parameter
    Parameter characterizing microscopic structure of quantum foam; its value enters the exact relationship and is tied to cosmographic data.
  • Tsallis nonextensive parameter
    Parameter for macroscopic nonextensive effects; linked exactly to the foam parameter through the cosmographic method.
axioms (1)
  • domain assumption Barrow-Tsallis entropy accounts for both quantum gravitational effects and nonextensive effects inherent in long-range interactions
    Stated directly in the abstract as the foundation for the model.

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Reference graph

Works this paper leans on

49 extracted references · 49 canonical work pages · 1 internal anchor

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