Dissipative Unimodular Gravity: Linking Energy Diffusion to Bulk Viscosity as an Alternative to $Λ$CDM under DESI DR2 Data

TL;DR

This work extends unimodular gravity by incorporating dissipative processes in the matter sector through energy diffusion $Q$ and bulk viscosity $ξ$, with $Q=νH^{2}$ and $ξ=ξ_{0}|Q|^{1/2}=ξ_{0}^{ν}|H|$. An analytic $H(z)$ is derived for a flat late-time universe with dust-like matter and a positive integration-constant cosmological term, and the model is confronted with SNe Ia, CC, BAO (DESI DR2), gravitational lensing, and black hole shadow data via MCMC with Bayesian criteria. The results indicate that both dissipative UG and UG without dissipation are competitive with ΛCDM, with a nonzero diffusion parameter $ν$ favored by the data, and a best-fit $H_{0}$ near the local measurement value; however, model selection via BIC can prefer the simpler, non-dissipative UG in some combinations. The study suggests that very small energy nonconservation, encoded through $Q$, can be consistent with late-time cosmology and that UG’s integration-constant treatment of Λ offers a pathway to alleviating the cosmological constant problem, effectively realizing a running vacuum scenario within UG.

Abstract

In this paper, we explore a theoretical and observational study of the presence of viscosity in the Unimodular Gravity formalism, a pioneering approach that, to the best of our knowledge, has not been previously explored in this context. Specifically, we study a flat FLRW universe at late times, where matter experiences dissipative processes in the form of a bulk viscosity, in the framework of Eckart's theory, which is linked to the energy diffusion function $Q$ through the power law $ξ=ξ_{0}\left|Q\right|^{1/2}$, being $ξ_{0}$ a positive dimensionless parameter. By assuming the ansatz $Q=νH^{2}$, where $H$ is the Hubble parameter and $ν$ is a dimensionless arbitrary constant, we find analytical solutions for the cosmological evolution. We test these models against the most recent cosmological observations, including type Ia supernovae, baryon acoustic oscillations, cosmic chronometers, gravitational lensing, and black hole shadow data. Our results show that two of the tested models provide a significantly better fit to the data ($χ_{\text{min}}^{2}$) and remain as competitive as $Λ$CDM model according to the Bayesian Information Criterion. These findings, combined with the inherent ability of Unimodular Gravity to alleviate the cosmological constant problem, position dissipative UG as a robust and compelling alternative to the standard model, potentially suggesting that a very small but nontrivial energy nonconservation is compatible with the late-time observational data.

Figures (4)

• Figure 1: The posterior 1D distributions and joint marginalized regions for the free parameter space of the $\Lambda$CDM model, obtained via the MCMC analysis described in Section \ref{['sec:Constraints']}. The admissible joint regions correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ CL, respectively. The best-fit values for each free parameter are shown in Table \ref{['tab:best-fits']}.
• Figure 2: The posterior 1D distributions and joint marginalized regions for the free parameter space of the dissipative UG model, obtained via the MCMC analysis described in Section \ref{['sec:Constraints']}. The admissible joint regions correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ CL, respectively. The best-fit values for each free parameter are shown in Table \ref{['tab:best-fits']}.
• Figure 3: The posterior 1D distributions and joint marginalized regions for the free parameter space of the dissipative UG model with $\xi_{0}=1$ ($\xi_{0}^{\nu}=|\nu|^{1/2}$), obtained via the MCMC analysis described in Section \ref{['sec:Constraints']}. The admissible joint regions correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ CL, respectively. The best-fit values for each free parameter are shown in Table \ref{['tab:best-fits']}.
• Figure 4: The posterior 1D distributions and joint marginalized regions for the free parameter space of the UG model without dissipation, obtained via the MCMC analysis described in Section \ref{['sec:Constraints']}. The admissible joint regions correspond to the $1\sigma$, $2\sigma$, and $3\sigma$ CL, respectively. The best-fit values for each free parameter are shown in Table \ref{['tab:best-fits']}.