The Monotonicity of the Gravitational Entropy Scalar within Quiescent Cosmology

TL;DR

This paper demonstrates that within Quiescent Cosmology, gravitational entropy, as measured by a specific scalar, starts at zero at the initial singularity and increases over time, aligning with Penrose's hypothesis.

Contribution

It establishes the monotonic increase of gravitational entropy in Quiescent Cosmology, confirming its consistency with Penrose's Weyl Curvature Hypothesis.

Findings

Gravitational entropy at the initial singularity tends to zero.

Gravitational entropy increases as the universe evolves from the initial singularity.

Supports the idea that gravitational entropy behaves oppositely to conventional entropy.

Abstract

In this paper we show that Quiescent Cosmology [1, 2, 3] is consistent with Penrose's Weyl Curvature Hypothesis and the notion of gravitational entropy [4]. Gravitational entropy, from a conceptual point of view, acts in an opposite fashion to the more familiar notion of entropy. A closed system of gravitating particles will coalesce whereas a collection of gas particles will tend to diffuse; regarding increasing entropy, these two scenarios are identical. What has been shown previously [2, 3] is that gravitational entropy at the initial singularity predicted by Quiescent Cosmology - the Isotropic Past Singularity (IPS) - tends to zero. The results from this paper show that not only is this the case but that gravitational entropy increases as this singularity evolves. In the first section of this paper we present relevant background information and motivation. In the second section of this paper we present the main results of this paper. Our third section contains a discussion of how this result will inspire future research before we make concluding remarks in our final section.