Relative information entropy and Weyl curvature of the inhomogeneous Universe

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.

8 pages, matches the published version in Physical Review D

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• An Exploration of the Black Hole Entropy via the Weyl Tensor
• Gauss-Bonnet-Chern approach to the averaged Universe
• Lightcone Averaging and Precision Cosmology
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• Kullback-Leibler entropy and Penrose conjecture in the Lemaitre-Tolman-Bondi model
• Classical, quantum, and phenomenological aspects of dark energy models
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• Weyl Curvature Hypothesis in light of Quantum Backreaction at Cosmological Singularities or Bounces