arxiv: 2604.17523 · v1 · submitted 2026-04-19 · 🌀 gr-qc · hep-th

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Comment on Cosmological constraints on unimodular gravity models with diffusion (arXiv:2211.07424): thermodynamic inadmissibility of the H0 tension resolution mechanism

Mauricio Cataldo

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Pith reviewed 2026-05-10 05:50 UTC · model grok-4.3

classification 🌀 gr-qc hep-th

keywords unimodular gravitydiffusion modelsHubble tensionsecond law of thermodynamicseffective cosmological constantthermodynamic admissibilitycosmological modelsenergy flow

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The pith

Unimodular gravity diffusion models cannot ease the Hubble tension without violating the second law of thermodynamics.

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

The paper shows that diffusion terms added to unimodular gravity to let an effective cosmological constant grow and ease the H0 tension necessarily violate the second law. From the Gibbs equation applied to pressureless matter, the second law requires the diffusion function Q to decrease with time, which drives energy into the matter sector rather than out of it. This direction is the opposite of what is needed for a positive dot Lambda_eff. The resulting no-go result holds for any choice of Q(t) and rules out the entire class of such models.

Core claim

Starting from the Gibbs relation for pressureless matter, the analysis derives a thermodynamic admissibility condition that forces dot Q less than zero for the second law to hold. This condition directly precludes the positive time derivative of the effective cosmological term that the referenced models require to address the Hubble tension. The incompatibility is independent of the specific functional form of Q(t) and applies uniformly to the Lambda CDM plus diffusion models in unimodular gravity.

What carries the argument

The thermodynamic admissibility condition dot Q less than zero derived from the Gibbs equation, which enforces the direction of energy flow between the effective cosmological term and the matter sector.

If this is right

Any diffusion model with dot Lambda_eff greater than zero must have dot Q greater than zero, violating the second law.
Energy must flow from the effective cosmological term into the matter sector to satisfy thermodynamics, blocking the required growth of Lambda_eff.
The result is structural and applies to every member of the Lambda CDM plus diffusion class with pressureless matter.
The models proposed in the referenced works are explicitly ruled out by this condition.

Where Pith is reading between the lines

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

Allowing a non-pressureless equation of state for the matter fluid might evade the thermodynamic obstruction.
The constraint points toward the need for entirely different mechanisms, without diffusion, to modify the effective cosmological term.
Similar thermodynamic checks could be applied to other proposed resolutions of the Hubble tension that involve energy exchange between sectors.

Load-bearing premise

The matter sector is treated as a pressureless fluid that continues to obey the standard Gibbs thermodynamic relation even after the diffusion term is introduced.

What would settle it

An explicit construction of a diffusion function Q(t) that produces dot Lambda_eff greater than zero while still satisfying the entropy non-decrease condition dot S greater than or equal to zero would falsify the no-go theorem.

read the original abstract

We show that the diffusion-based models proposed in Refs.~\cite{Perez2021,Landau2022} within the framework of Unimodular Gravity (UG) to alleviate the $H_0$ tension are incompatible with the second law of thermodynamics. Starting from the Gibbs equation for a pressureless matter fluid, we derive a general thermodynamic admissibility condition for the $\Lambda$CDM$+$diffusion class in UG, demonstrating that the second law requires $\dot{Q} < 0$, independently of the specific form of the diffusion function $Q(t)$. This condition implies that energy must flow from the effective cosmological term $\Lambda_{\rm eff}$ into the matter sector, rather than in the opposite direction. We then establish a no-go theorem: no choice of $Q(t)$ can simultaneously satisfy the second law and generate the growing effective cosmological term $\dot{\Lambda}_{\rm eff} > 0$ required to alleviate the $H_0$ tension. We confirm this result explicitly for the models of Perez, Sudarsky, and Wilson-Ewing~\cite{Perez2021} and Landau et al.~\cite{Landau2022}, noting that the former explicitly identify $\dot{\Lambda}_{\rm eff} > 0$ as a necessary feature of their proposal without addressing its thermodynamic implications. The incompatibility is therefore structural and applies to the entire class of $\Lambda$CDM$+$diffusion models in UG with a pressureless matter component.

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.

Desk Editor's Note private letter to a colleague

This comment derives a no-go theorem showing that diffusion in unimodular gravity cannot fix the H0 tension thermodynamically.

read the letter

This comment paper establishes that diffusion models in unimodular gravity cannot resolve the H0 tension without violating the second law of thermodynamics. No Q(t) works for both the required sign on the diffusion term and the growing effective Lambda. It does a solid job deriving the general admissibility condition from the Gibbs equation for pressureless matter, leading to dot Q < 0. This forces energy transfer in the wrong direction for the models' needs. The explicit checks on the Perez and Landau papers make the incompatibility clear and structural for the class. The soft spot lies in assuming the standard Gibbs relation holds without change despite the diffusion source. The non-conservation of the matter tensor might introduce modifications to the thermodynamic identity or additional entropy terms, and the paper does not detail why this does not occur. That assumption drives the no-go, so it merits close examination. This note is for specialists in modified gravity cosmologies and H0 tension proposals. Readers focused on thermodynamic consistency will find it directly useful. It shows honest engagement with the cited works and a clear logical chain. I recommend sending it to peer review. The critique is targeted enough to warrant referee input on the thermodynamic steps.

Referee Report

1 major / 0 minor

Summary. The manuscript is a comment arguing that diffusion-based unimodular gravity models proposed to resolve the H0 tension (specifically those in Perez et al. 2021 and Landau et al. 2022) are thermodynamically inadmissible. Starting from the Gibbs equation for pressureless matter, it derives that the second law requires dot{Q} < 0 independently of the form of Q(t), implying energy flow from Lambda_eff to matter; this directly contradicts the dot{Lambda}_eff > 0 needed for H0 alleviation, yielding a structural no-go theorem for the entire LambdaCDM + diffusion class in UG.

Significance. If the central derivation holds, the result is significant: it supplies a general thermodynamic obstruction to a specific mechanism for addressing the Hubble tension within unimodular gravity, backed by explicit verification on the two cited models. This could usefully constrain future work on diffusion or non-conservation terms in modified cosmologies. The argument is parameter-free and relies on standard thermodynamic identities rather than fits.

major comments (1)

[Abstract and derivation of thermodynamic admissibility condition] The derivation of the sign condition dot{Q} < 0 (abstract and the section applying the Gibbs equation to the modified continuity equation): the manuscript assumes without explicit justification that the standard Gibbs relation T dS = d(rho V) for p=0 remains valid for the matter sector even though the diffusion term induces non-conservation of the matter energy-momentum tensor. This assumption is load-bearing for the no-go theorem, as the sign on dot{Q} follows directly from it; a brief discussion of why local thermodynamic equilibrium persists or why no additional entropy flux arises from the diffusion process would strengthen the claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and constructive comment on our manuscript. We address the major comment below and will revise the manuscript to incorporate a clarifying discussion as suggested.

read point-by-point responses

Referee: [Abstract and derivation of thermodynamic admissibility condition] The derivation of the sign condition dot{Q} < 0 (abstract and the section applying the Gibbs equation to the modified continuity equation): the manuscript assumes without explicit justification that the standard Gibbs relation T dS = d(rho V) for p=0 remains valid for the matter sector even though the diffusion term induces non-conservation of the matter energy-momentum tensor. This assumption is load-bearing for the no-go theorem, as the sign on dot{Q} follows directly from it; a brief discussion of why local thermodynamic equilibrium persists or why no additional entropy flux arises from the diffusion process would strengthen the claim.

Authors: We appreciate the referee's observation that the validity of the Gibbs relation under non-conservation is central to the derivation. In our analysis, the diffusion term Q(t) represents a phenomenological energy exchange between the matter sector and the effective cosmological constant, while the matter fluid is modeled as remaining in local thermodynamic equilibrium. The local identity T dS = d(ρ V) for pressureless matter therefore continues to apply to the dust component, with the non-conservation entering only through the modified continuity equation; this is consistent with standard treatments of interacting fluids in cosmology. We agree, however, that an explicit justification would strengthen the presentation. In the revised manuscript we will add a brief paragraph in the relevant section explaining the persistence of local thermodynamic equilibrium for the matter sector and the absence of additional entropy fluxes arising from the diffusion process. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies standard thermodynamic identities to the model's continuity equation without reducing to self-definition or fitted inputs.

full rationale

The paper derives a no-go theorem by starting from the Gibbs equation T dS = d(ρV) for pressureless fluid and applying it to the matter continuity equation modified by the diffusion term Q(t) in unimodular gravity. This yields the condition dot Q < 0 required by the second law, which is incompatible with dot Lambda_eff > 0. No step involves fitting parameters to data and relabeling as prediction, self-citation of the authors' own uniqueness theorems, or redefining quantities in terms of the target result. The argument relies on external thermodynamic principles and the equations of the target models, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the applicability of the standard Gibbs equation to pressureless matter in the presence of diffusion within unimodular gravity; no free parameters or new entities are introduced.

axioms (2)

domain assumption Gibbs equation for a pressureless matter fluid
Invoked at the start of the derivation to obtain the thermodynamic admissibility condition.
standard math Second law of thermodynamics requires non-negative entropy production
Used to derive the requirement dot Q < 0.

pith-pipeline@v0.9.0 · 5581 in / 1293 out tokens · 46528 ms · 2026-05-10T05:50:12.802336+00:00 · methodology

discussion (0)

Reference graph

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