Time evolution of the mutual information between disjoint regions in the Universe

TL;DR

This paper investigates how the mutual information between separated regions in the universe evolves over time, revealing its dependence on cosmic expansion and dark energy, and suggesting potential links to the universe's accelerated expansion.

Contribution

It introduces a study of the time evolution of mutual information in cosmological contexts, highlighting its relation to dark energy and universe dynamics.

Findings

Mutual information decreases over time in a matter-dominated universe.

It remains constant in a Λ-dominated universe.

Predicts a minimum in mutual information indicating dark energy influence.

Abstract

We study the time evolution of the mutual information between the mass distributions in spatially separated but casually connected regions in an expanding universe. The evolution of the mutual information is primarily determined by the configuration entropy rate which depends on the dynamics of the expansion and the growth of the density perturbations. The joint entropy between the distributions from the two regions plays a negligible role in such evolution. The mutual information decreases with time in a matter dominated Universe whereas it stays constant in a $\Lambda$-dominated Universe. The $\Lambda$CDM model and some other models of dark energy predict a minimum in the mutual information beyond which the dark energy dominates the dynamics of the Universe. The mutual information may have deeper connections to the dark energy and the accelerated expansion of the universe.