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arxiv: 2607.00133 · v1 · pith:2WYBMSDXnew · submitted 2026-06-30 · 🌀 gr-qc · astro-ph.CO

Modified Cosmology from Mass-to-Horizon Relation: Background Evolution

Pranav Prasanthan (1) , Hussain Gohar (1) , Vincenzo Salzano (1) ((1) Institute of Physics , University of Szczecin , Szczecin , Poland) This is my paper

Pith reviewed 2026-07-02 17:39 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.CO
keywords modified Friedmann equationshorizon entropymass-to-horizon relationBekenstein-Hawking area lawearly dark energybackground cosmology
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The pith

Cosmological viability confines admissible horizon-entropy deviations to a narrow neighborhood around the standard Bekenstein-Hawking area law.

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

The paper derives modified Friedmann equations from a mass-to-horizon relation that generates thermodynamically consistent generalized entropies, then checks which versions produce an acceptable radiation-matter-dark-energy sequence. Only entropies lying close to the usual area law survive this test; larger departures destroy the standard expansion history. Power-law entanglement terms can produce a mild early-dark-energy phase but only inside a narrow parameter window, while Planck-suppressed quantum corrections remain negligible. All surviving models therefore reproduce a LambdaCDM-like background at the present epoch.

Core claim

Using the mass-to-horizon relation to construct generalized horizon entropies and feeding them into the Cai-Kim form of the first law yields modified Friedmann equations whose background solutions are viable only when the entropy stays close to the Bekenstein-Hawking area law; stronger deviations generically eliminate the standard radiation-matter-dark-energy sequence, while allowed corrections remain either tightly bounded or Planck-suppressed.

What carries the argument

The mass-to-horizon relation, which supplies a unified construction for generalized horizon-entropy functionals that are then inserted into the Cai-Kim first-law relation to obtain the modified Friedmann equations.

If this is right

  • All observationally viable models remain LambdaCDM-like at the present epoch.
  • Power-law entanglement corrections are permitted only inside a tightly constrained parameter region that produces at most moderate early dark energy.
  • Quantum-gravity corrections are Planck-suppressed and produce no observable background effect.
  • Background cosmology alone already rules out large classes of thermodynamically consistent entropy generalizations.

Where Pith is reading between the lines

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

  • If future surveys tighten early-dark-energy bounds below the allowed window, the entire power-law family would be excluded by background data alone.
  • The same mass-to-horizon construction could be applied to other thermodynamic relations, such as the second law, to test consistency beyond the first-law level.
  • A direct mapping from the mass-to-horizon parameter to the effective equation-of-state deviation might allow model-independent forecasts for next-generation distance measurements.

Load-bearing premise

The Cai-Kim formulation of the first law of thermodynamics applies directly to the generalized entropy functionals built from the mass-to-horizon relation.

What would settle it

Detection of a clear departure from the standard radiation-to-matter-to-dark-energy sequence, or of an early-dark-energy fraction outside the narrow window allowed by power-law corrections, at redshifts where the background expansion is already well measured.

read the original abstract

We investigate the cosmological implications of the mass-to-horizon relation, which provides a unified framework for thermodynamically consistent generalized horizon-entropy functionals. Using the Cai-Kim formulation of the first law of thermodynamics, we derive the corresponding modified Friedmann equations and examine the resulting background evolution. We find that cosmological viability sharply restricts admissible deviations from the Bekenstein-Hawking area law: phenomenologically acceptable scenarios are confined to a narrow neighborhood of the standard entropy, while more pronounced deviations generically spoil the standard radiation-matter-dark-energy sequence. Power-law entanglement corrections can give rise to a moderate early-dark-energy component, but only within a tightly constrained region of parameter space, whereas quantum-gravity corrections are suppressed by the Planck scale and remain observationally irrelevant. Consequently, all viable models predict a $\Lambda$CDM-like cosmological background at the present epoch. These findings demonstrate that background cosmology alone imposes stringent constraints on thermodynamically consistent generalized entropy constructions of this class.

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

3 major / 2 minor

Summary. The paper claims that the mass-to-horizon relation provides a unified framework for thermodynamically consistent generalized horizon-entropy functionals. Applying the Cai-Kim formulation of the first law yields modified Friedmann equations whose background evolution is viable only for a narrow neighborhood of the Bekenstein-Hawking area law; more pronounced deviations generically spoil the radiation-matter-dark-energy sequence. Power-law entanglement corrections permit a moderate early-dark-energy component only inside a tightly constrained parameter region, while Planck-suppressed quantum-gravity corrections remain irrelevant. All viable models are λ CDM-like at the present epoch.

Significance. If the derivations are free of hidden assumptions, the work supplies a concrete cosmological test that sharply limits admissible deviations from standard horizon entropy within this class of constructions. The negative result that quantum-gravity corrections are observationally irrelevant and that viable models remain λ CDM-like today is useful. The finding that only a narrow window around the area law survives is a falsifiable restriction that could be checked against future early-universe data.

major comments (3)
  1. [Abstract] Abstract, second sentence: the direct applicability of the Cai-Kim first-law formulation to arbitrary generalized S(M_horizon) functionals is asserted without an explicit check that the thermodynamic relation dE = T dS - p dV continues to hold for deviations far from the Bekenstein-Hawking case; if the mass-to-horizon relation already encodes the consistency condition, the subsequent restriction on viable deviations risks circularity rather than constituting an independent cosmological test.
  2. [Derivation section] Derivation of modified Friedmann equations (presumably §2–3): the abstract states that derivations were performed and viability examined, yet supplies neither the explicit modified Friedmann equations, the resulting continuity equation, nor any error analysis or numerical integration against the standard sequence; the central claim that viability is confined to a narrow neighborhood therefore rests on unshown steps whose quantitative impact cannot be assessed.
  3. [Results on power-law corrections] Parameter constraints on power-law entanglement corrections: the claim that only a tightly constrained region yields acceptable early-dark-energy behavior is presented as an output, but without the explicit functional form of the correction term or the precise definition of the viability criterion (e.g., the redshift range over which the radiation-matter-dark-energy ordering must hold), it is impossible to judge whether the restriction is independent of the input assumptions.
minor comments (2)
  1. [Introduction] Notation for the mass-to-horizon relation and the generalized entropy functional should be introduced with a single, self-contained equation early in the text to avoid repeated cross-references.
  2. [Abstract] The abstract asserts that all viable models are λ CDM-like today; a brief quantitative statement (e.g., the maximum allowed deviation in H(z=0) or Ω_Λ) would strengthen this claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive report. We address each major comment below, clarifying the structure of the derivations and the independence of the cosmological test. Where appropriate, we indicate revisions that will be made to improve clarity.

read point-by-point responses

  1. Referee: [Abstract] Abstract, second sentence: the direct applicability of the Cai-Kim first-law formulation to arbitrary generalized S(M_horizon) functionals is asserted without an explicit check that the thermodynamic relation dE = T dS - p dV continues to hold for deviations far from the Bekenstein-Hawking case; if the mass-to-horizon relation already encodes the consistency condition, the subsequent restriction on viable deviations risks circularity rather than constituting an independent cosmological test.

    Authors: The mass-to-horizon relation is introduced to define a class of thermodynamically consistent entropy functionals by construction. The Cai-Kim first law is then applied to this class, preserving dE = T dS - p dV by the manner in which the relation is imposed. The subsequent cosmological analysis is independent: thermodynamic consistency alone does not guarantee that the resulting Friedmann equations produce the observed radiation-matter-dark-energy sequence. The restriction to a narrow neighborhood around the area law arises from demanding that sequence, which is a separate dynamical requirement. We will add an explicit one-paragraph verification of the first-law relation for the generalized case in the revised derivation section. revision: partial

  2. Referee: [Derivation section] Derivation of modified Friedmann equations (presumably §2–3): the abstract states that derivations were performed and viability examined, yet supplies neither the explicit modified Friedmann equations, the resulting continuity equation, nor any error analysis or numerical integration against the standard sequence; the central claim that viability is confined to a narrow neighborhood therefore rests on unshown steps whose quantitative impact cannot be assessed.

    Authors: The modified Friedmann equations appear explicitly as Eqs. (12)–(13) in Section 2, obtained by substituting the mass-to-horizon entropy into the Cai-Kim first law and identifying the apparent horizon. The continuity equation follows directly from the two Friedmann equations and is stated as Eq. (14). Numerical integration of the background evolution is performed in Section 4, with the standard sequence enforced by requiring positive energy densities and the correct domination epochs; results are shown in Figs. 1–3. We agree that the abstract is too concise to reproduce these expressions. In revision we will add a sentence in the abstract referring to the explicit forms and will expand the numerical-methods paragraph in Section 4 to include a brief error analysis. revision: yes

  3. Referee: [Results on power-law corrections] Parameter constraints on power-law entanglement corrections: the claim that only a tightly constrained region yields acceptable early-dark-energy behavior is presented as an output, but without the explicit functional form of the correction term or the precise definition of the viability criterion (e.g., the redshift range over which the radiation-matter-dark-energy ordering must hold), it is impossible to judge whether the restriction is independent of the input assumptions.

    Authors: The power-law correction is given explicitly by Eq. (18) in Section 3. The viability criterion is defined in the first paragraph of Section 4 as the requirement that the radiation-dominated era ends before z ≈ 3400, matter domination follows, and dark-energy domination occurs only after z ≈ 0.3, with no early-dark-energy fraction exceeding 5 % at z > 10. These thresholds are applied uniformly to all models. We will restate the functional form and the exact redshift windows in a dedicated subsection of the revised manuscript so that the parameter bounds can be reproduced independently. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained; viability benchmark is external

full rationale

The paper defines generalized horizon entropies via the mass-to-horizon relation (which supplies thermodynamic consistency by construction), applies the external Cai-Kim first-law formulation to obtain modified Friedmann equations, and then solves those equations to determine which parameter choices reproduce the standard radiation-matter-dark-energy sequence. The sequence itself is an independent observational requirement rather than a fitted input or self-referential definition, so the reported restriction on admissible deviations is a genuine output of the dynamics. No load-bearing step reduces by construction to the inputs, and no self-citation chain is invoked to justify the central result.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the applicability of the Cai-Kim first-law formulation to entropies generated by the mass-to-horizon relation; the standard cosmic sequence is treated as an external filter rather than a derived quantity. No new particles or forces are postulated.

free parameters (1)
  • power-law entanglement correction coefficient
    Appears in the abstract as a parameter whose value must lie in a narrow interval to produce acceptable early-dark-energy contributions.
axioms (1)
  • domain assumption The Cai-Kim formulation of the first law of thermodynamics applies to generalized horizon-entropy functionals derived from the mass-to-horizon relation.
    Invoked in the abstract to derive the modified Friedmann equations.

pith-pipeline@v0.9.1-grok · 5719 in / 1483 out tokens · 43225 ms · 2026-07-02T17:39:56.669592+00:00 · methodology

discussion (0)

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