Unimodular Diffusion and Interacting Vacuum Cosmology

TL;DR

This paper explores the connection between unimodular diffusion cosmology and interacting dark energy models, analyzing background and perturbation levels with observational data, and finds that diffusion models can mimic certain interacting vacuum scenarios.

Contribution

It demonstrates that unimodular diffusion cosmology can be mapped onto interacting vacuum models at the background level and constrains the interaction parameter using cosmological data.

Findings

Diffusion framework compatible with interacting vacuum models with homogeneous energy transfer.

Best-fit interaction parameter $\xi$ close to zero, consistent with $ abla$CDM.

Modest impact on structure growth, with $S_8$ similar to $ abla$CDM.

Abstract

We investigate the correspondence between unimodular diffusion cosmology and interacting dark sector models at the background and linear perturbation levels. In the diffusion framework, the effective cosmological constant becomes time dependent, $\Lambda(t)$, sourced by a diffusion current. We show that at the background level this framework can be mapped onto interacting dark energy models with $w=-1$ and energy transfer $Q$. Using two common parameterizations, $Q = \xi H \rho_{\rm de}$ and $Q = \xi H \rho_{\rm dm}$, and data from supernovae, DESI BAO, cosmic chronometers, and CMB distance priors, we find $\xi = -0.0197 \pm 0.0076$ for the vacuum-coupled case, while the matter-coupled case gives a best-fit $\xi = 0.0018$ with comparable goodness of fit. At the level of linear perturbations, however, the diffusion framework is consistent only with interacting vacuum models having homogeneous energy transfer ($Q \propto \rho_{\rm de}$ with $\delta Q=0$), thereby breaking the degeneracy with more general interacting dark energy scenarios. Including redshift-space distortion data, we obtain $\xi = -0.0147 \pm 0.0075$, consistent with $\Lambda$CDM ($\xi=0$) at $2\sigma$. The inferred clustering amplitude is $S_8 = 0.782 \pm 0.026$ for the diffusion model, compared to $S_8 = 0.77 \pm 0.025$ for $\Lambda$CDM under the same dataset, indicating a modest but non-negligible impact on structure growth.