Relative information entropy of an inhomogeneous universe

TL;DR

This paper introduces a measure based on relative information entropy to quantify inhomogeneities in the universe, exploring its evolution and connection to gravitational entropy and backreaction effects.

Contribution

It proposes a natural measure for inhomogeneous cosmological models using Kullback-Leibler entropy and analyzes its time evolution in linear and nonlinear regimes.

Findings

The measure tends to increase over time in cosmological models.

The measure's behavior is linked to gravitational entropy and inhomogeneity backreaction.

Conditions for the measure's increase are discussed in various cosmological contexts.

Abstract

In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field from its spatial average on arbitrary compact domains. This measure is expected to be an increasing function in time and thus to play a significant role in studying gravitational entropy. To verify this conjecture, we explore the time evolution of the measure using the linear perturbation theory of a spatially flat FLRW model and a spherically symmetric nonlinear solution. We discuss the generality and conditions for the time-increasing nature of the measure, and also the connection to the backreaction effect caused by inhomogeneities.