Cosmological evolution of the gravitational entropy of the large-scale structure

TL;DR

This paper investigates the evolution of gravitational entropy in the universe's large-scale structure, comparing different definitions and averaging methods, revealing growth and saturation behaviors in various cosmological models.

Contribution

It introduces a comparative analysis of two entropy definitions in linear cosmological perturbation theory, highlighting their different temporal behaviors in CDM and ΛCDM models.

Findings

Entropy grows over time in both models.

Entropy diverges in CDM but saturates in ΛCDM.

Light-cone averaging affects entropy evaluation.

Abstract

We consider the entropy associated with the large-scale structure of the Universe in the linear regime, where the Universe can be described by a perturbed Friedmann-Lema\^itre spacetime. In particular, we compare two different definitions proposed in the literature for the entropy using a spatial averaging prescription. For one definition, the entropy of the large-scale structure for a given comoving volume always grows with time, both for a CDM and a $\Lambda$CDM model. In particular, while it diverges for a CDM model, it saturates to a constant value in the presence of a cosmological constant. The use of a light-cone averaging prescription in the context of the evaluation of the entropy is also discussed.