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

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.