Information Entropy in Cosmology

TL;DR

This paper explores the concept of information entropy in cosmology, proposing that the universe's information content, measured by relative entropy, likely increases over time, reflecting the growth of inhomogeneities.

Contribution

It introduces a measure of information entropy based on the Kullback-Leibler divergence to describe inhomogeneous cosmological models and discusses its time evolution.

Findings

The information measure aligns with the Kullback-Leibler entropy in cosmology.

The universe's information content is conjectured to increase over time.

The measure provides insights into the growth of inhomogeneities in the universe.

Abstract

The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the `Kullback-Leibler Relative Information Entropy', expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time-evolution of `effective information' and explore some implications. We conjecture that the information content of the Universe -- measured by Relative Information Entropy of a cosmological model containing dust matter -- is increasing.