Gravitational Entropy and Quantum Cosmology

TL;DR

This paper explores gravitational entropy measures in cosmological models, introduces a new thermodynamic-compatible quantity, and examines quantum initial conditions supporting Penrose's Weyl Curvature Conjecture using the Wheeler-DeWitt equation.

Contribution

It introduces a new gravitational entropy measure consistent with thermodynamics and assesses quantum initial conditions for the universe related to Penrose's conjecture.

Findings

A new entropy measure obeys the second law in cosmological models

Local version of the conjecture does not support Penrose's idea

A non-local entity shows promising behavior supporting the conjecture

Abstract

We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part of the curvature dominates over the Weyl part at the initial singularity of the universe. The theory is applied to the Bianchi type I universe models with dust and a cosmological constant and to the Lema\^itre-Tolman universe models. We investigate two different versions of the conjecture. First we investigate a local version which fails to support the conjecture. Thereafter we construct a non-local entity which shows more promising behaviour concerning the conjecture.