An investigation on gravitational entropy of cosmological models

TL;DR

This paper explores gravitational entropy in cosmological models using a specific definition, examining how it evolves near singularities and its relation to structure formation, thereby testing Penrose's Weyl curvature hypothesis.

Contribution

It applies a particular gravitational entropy measure to various cosmological models to analyze the validity of Penrose's conjecture near singularities.

Findings

Gravitational entropy increases monotonically in certain models.

Conditions for the validity of Weyl curvature hypothesis are identified.

Near initial singularity, the ratio of free gravity energy density to matter density approaches zero.

Abstract

In this paper, we investigate the entropy of the free gravitational field for a given epoch for some well-known isotropic and anisotropic cosmologies. We use the definition of gravitational entropy proposed by Clifton, Ellis, and Tavakol, where the 2-index square root of the 4-index Bel-Robinson tensor is taken to be the energy momentum tensor for the free gravity. We examine whether, in the vicinity of the initial singularity, the ratio of the energy density of free gravity to that of matter density goes to zero, validating Penrose's conjecture on Weyl curvature. Whenever this is true, the gravitational entropy increases monotonically with time, leading to structure formation. For the models considered by us, we identify the conditions for which the Weyl curvature hypothesis is valid, and the assumptions under which it is validated, or otherwise.