Relative information entropy and Weyl curvature of the inhomogeneous Universe

TL;DR

This paper explores the relationship between entropy and Weyl curvature in the universe, using cosmological perturbation theory to quantify deviations from homogeneity and isotropy, and linking these measures to the universe's large-scale structure formation.

Contribution

It introduces and analyzes two scalar measures of inhomogeneity, demonstrating their correlation and connection through kinematic backreaction in cosmological models.

Findings

The measures are correlated during structure formation.

They can be linked via the kinematic backreaction.

Quantitative relations are established up to second order in perturbation theory.

Abstract

Penrose conjectured a connection between entropy and Weyl curvature of the Universe. This is plausible, as the almost homogeneous and isotropic Universe at the onset of structure formation has negligible Weyl curvature, which then grows (relative to the Ricci curvature) due to the formation of large-scale structure and thus reminds us of the second law of thermodynamics. We study two scalar measures to quantify the deviations from a homogeneous and isotropic space-time, the relative information entropy and a Weyl tensor invariant, and show their relation to the averaging problem. We calculate these two quantities up to second order in standard cosmological perturbation theory and find that they are correlated and can be linked via the kinematic backreaction of a spatially averaged universe model.