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

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.