Relative information entropy and Weyl curvature of the inhomogeneous Universe
Penrose conjectured a connection between entropy and Weyl curvature of theUniverse. This is plausible, as the almost homogeneous and isotropic Universeat the onset of structure formation has negligible Weyl curvature, which thengrows (relative to the Ricci curvature) due to the formation of large-scalestructure and thus reminds us of the second law of thermodynamics. We study twoscalar measures to quantify the deviations from a homogeneous and isotropicspace-time, the relative information entropy and a Weyl tensor invariant, andshow their relation to the averaging problem. We calculate these two quantitiesup to second order in standard cosmological perturbation theory and find thatthey are correlated and can be linked via the kinematic backreaction of aspatially averaged universe model.
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American Physical Society (APS)