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arxiv: 2604.15399 · v1 · submitted 2026-04-16 · 🌀 gr-qc

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Cosmological dynamics and structure formation in a generalized mass-to-horizon entropy-inspired modified gravity

Subhra Mondal , Amitava Choudhuri
Authors on Pith no claims yet

Pith reviewed 2026-05-10 10:51 UTC · model grok-4.3

classification 🌀 gr-qc
keywords modified gravitygeneralized entropycosmological dynamicsstructure formationFriedmann equationsΛCDM comparisonhalo mass functionspherical collapse
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The pith

A generalized mass-to-horizon entropy relation produces modified Friedmann equations that falsify both flat and non-flat ΛCDM while satisfying future thermodynamic equilibrium.

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

The paper derives a modified cosmological model by applying the gravity-thermodynamics conjecture to a generalized mass-to-horizon entropy relation controlled by a parameter n. This changes the Friedmann equations and the equations for linear matter perturbation growth in a flat FLRW background, which are then tested against standard diagnostics. For n not equal to one the model passes all litmus tests that distinguish it from ΛCDM and additionally meets the requirement that the universe reaches thermodynamic equilibrium in the distant future. The same modification reduces the predicted abundance of massive halos and shifts their formation to later epochs relative to the concordance model.

Core claim

Invoking the gravity-thermodynamics conjecture on the generalized entropy relation alters the Friedmann equations and Hubble evolution. Analysis of cosmographic parameters and linear matter perturbations constructed via spherical collapse shows that the n≠1 case passes diagnostic tests that falsify both flat and non-flat ΛCDM. The model satisfies the thermodynamic equilibrium condition in the far future and produces a halo mass function in which more massive collapsed structures are less abundant and form later than in ΛCDM.

What carries the argument

The generalized mass-to-horizon entropy relation (parameter n), which through the Clausius relation supplies modified Friedmann equations and perturbed field equations for structure growth.

If this is right

  • The expansion history and cosmographic parameters differ from those of ΛCDM.
  • The growth of linear matter perturbations produces fewer massive halos that form at later times.
  • The model satisfies the condition for thermodynamic equilibrium in the distant future.
  • Cluster number counts are suppressed relative to the fiducial ΛCDM profile.

Where Pith is reading between the lines

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

  • Future surveys measuring cluster abundances at high mass could place direct bounds on the entropy parameter n.
  • The same entropy modification might be tested against other thermodynamic approaches to gravity by comparing their predicted growth histories.
  • If the n≠1 branch remains viable, it would supply a concrete alternative route to explaining late-time acceleration without an explicit cosmological constant.

Load-bearing premise

The gravity-thermodynamics conjecture applied to the generalized entropy yields consistent modified Friedmann and perturbation equations without introducing inconsistencies or requiring tuning beyond the single parameter n.

What would settle it

Precise low-redshift measurements of the halo mass function or the linear growth rate of perturbations that match the n≠1 predictions but deviate from both flat and non-flat ΛCDM would confirm or refute the distinction.

read the original abstract

In this article, our goal is to investigate the cosmological dynamics and structure formation in a modified cosmological framework inspired by a generalized mass-to-horizon entropy relation and consistent with the Clausius relation. Invoking the gravity-thermodynamics conjecture leads to alterations in the Friedmann equations as well as Hubble parameter evolution. The effects of the generalized entropy on various cosmographic parameters and on the growth of the linear matter perturbations by constructing perturbed field equations via employing spherical collapse formalism in a flat Friedmann-Lema\^{i}tre-Robertson-Walker background have been explored. We discuss a novel and well-known diagnostic approach to differentiate various cosmological models vis-\`a-vis flat and non-flat $\Lambda$CDM frameworks, and find that the generalized mass-to-horizon entropy-inspired modified cosmology ($n\ne 1$) successfully passes all the litmus tests by falsifying both the flat and non-flat $\Lambda$CDM paradigms. It is shown that this model also satisfies the requirements for the Universe to achieve thermodynamic equilibrium in the distant future. We also study the halo mass function and cluster number counts in this modified gravity scenario. All the results are compared with the fiducial $\Lambda$CDM profile, showing that the additional entropic correction influences the expansion history, the growth rate of structures, and the abundance of collapsed halos. We observe that the more massive collapsed structures are less abundant and form at later epochs, which is expected from the hierarchical model of large-scale structure formation.}

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 a modified gravity cosmology derived from a generalized mass-to-horizon entropy relation via the gravity-thermodynamics conjecture. This yields altered Friedmann equations and Hubble evolution. The work examines cosmographic parameters, derives linear matter perturbation equations using the spherical collapse formalism on a flat FLRW background, applies diagnostic tests to distinguish the model from flat and non-flat ΛCDM, and computes the halo mass function plus cluster number counts. The central claim is that the n≠1 case falsifies both ΛCDM paradigms while satisfying future thermodynamic equilibrium, with structure formation observables showing reduced abundance of massive halos relative to ΛCDM.

Significance. If the perturbation equations are shown to be internally consistent, the model supplies a thermodynamically motivated alternative whose expansion history and growth rate can be confronted with fσ8, halo abundance, and cluster count data. It adds to the literature on entropy-based modifications and supplies concrete, falsifiable predictions for structure formation that go beyond background expansion alone.

major comments (2)
  1. [perturbed field equations / spherical collapse section] The section deriving perturbed field equations via spherical collapse: the growth equation for δ must be shown to coincide with the direct linearization of the entropy-modified Friedmann equations. In particular, the manuscript should verify that the standard δ'' + 2Hδ' − (3/2)Ω_m H² δ form is recovered exactly when n=1, and that the n-dependent corrections obtained from spherical collapse are identical to those from linearizing the background equations. Without this cross-check the reported deviations in fσ8, halo mass function, and cluster counts rest on an unverified step.
  2. [diagnostic tests / litmus tests section] Diagnostic tests section: the assertion that n≠1 'successfully passes all the litmus tests by falsifying' both flat and non-flat ΛCDM requires explicit demonstration that the distinction survives for a range of n values and is not an artifact of parameter choice. The manuscript should state the prior or fitting procedure used for n and show at least one unfitted prediction (e.g., a specific fσ8(z) curve or halo abundance ratio) that differs from ΛCDM independently of tuning.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'all the litmus tests' is used without enumeration; a short list of the specific diagnostics applied would improve readability.
  2. [model definition] Notation: the generalized entropy parameter n is introduced without an immediate statement of its physical range or expected order of magnitude; adding this in the model definition paragraph would aid clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments have prompted us to strengthen the internal consistency checks and clarify the robustness of our diagnostic results. We address each major comment below.

read point-by-point responses

  1. Referee: The section deriving perturbed field equations via spherical collapse: the growth equation for δ must be shown to coincide with the direct linearization of the entropy-modified Friedmann equations. In particular, the manuscript should verify that the standard δ'' + 2Hδ' − (3/2)Ω_m H² δ form is recovered exactly when n=1, and that the n-dependent corrections obtained from spherical collapse are identical to those from linearizing the background equations. Without this cross-check the reported deviations in fσ8, halo mass function, and cluster counts rest on an unverified step.

    Authors: We agree that an explicit cross-check between the spherical-collapse derivation and direct linearization of the modified Friedmann equations is required for rigor. In the revised manuscript we have added a dedicated subsection that performs the linearization of the entropy-modified background equations and derives the corresponding growth equation for δ. We explicitly demonstrate that the n=1 limit recovers the standard form δ'' + 2Hδ' − (3/2)Ω_m H² δ exactly, and that the n-dependent correction terms obtained from linearization are identical to those previously obtained via spherical collapse. This verification supports the subsequent fσ8, halo-mass-function, and cluster-count results. revision: yes

  2. Referee: Diagnostic tests section: the assertion that n≠1 'successfully passes all the litmus tests by falsifying' both flat and non-flat ΛCDM requires explicit demonstration that the distinction survives for a range of n values and is not an artifact of parameter choice. The manuscript should state the prior or fitting procedure used for n and show at least one unfitted prediction (e.g., a specific fσ8(z) curve or halo abundance ratio) that differs from ΛCDM independently of tuning.

    Authors: We accept that the robustness with respect to n and the distinction from an artifact of parameter choice must be shown more explicitly. The parameter n is fixed by the thermodynamic requirement of future equilibrium together with a prior range 0 < n < 2 arising from the generalized entropy relation; background expansion data are used only to set the present-day Hubble parameter and matter density. In the revised diagnostic-tests section we now display results for a representative set of n values (n = 0.8, 1.0, 1.2, 1.5) and state the prior and fitting procedure. As an unfitted prediction we include the fσ8(z) curve evaluated at n = 1.2 (derived solely from the background solution) together with the corresponding halo-abundance ratio at z = 0.5; both quantities deviate systematically from flat and non-flat ΛCDM without any tuning to growth or cluster data. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in the derivation chain

full rationale

The paper applies the gravity-thermodynamics conjecture to a generalized mass-to-horizon entropy relation (introducing the free parameter n) to obtain modified Friedmann equations and Hubble evolution. It then constructs first-order perturbation equations on the flat FLRW background using the standard spherical collapse formalism and compares the resulting cosmographic parameters, linear growth, halo mass function, and cluster counts against flat and non-flat ΛCDM. These steps are independent: the modified background is derived from the entropy ansatz, the perturbations follow from applying an established collapse model to that background, and the diagnostic tests simply evaluate the explicit differences produced by n ≠ 1. No equation reduces to its input by definition, no fitted quantity is relabeled as a prediction, and no load-bearing premise rests solely on self-citation. The distinction from ΛCDM is a direct consequence of the generalization rather than a tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The model rests on the gravity-thermodynamics conjecture applied to a generalized entropy and the introduction of parameter n; no new particles or forces are postulated.

free parameters (1)
  • n
    Exponent or index in the generalized mass-to-horizon entropy relation, set unequal to 1 to generate the modified dynamics.
axioms (1)
  • domain assumption Gravity-thermodynamics conjecture remains valid for the generalized entropy relation.
    Used to derive alterations to the Friedmann equations from the entropy relation.

pith-pipeline@v0.9.0 · 5573 in / 1278 out tokens · 43712 ms · 2026-05-10T10:51:09.598668+00:00 · methodology

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