Relative information entropy of an inhomogeneous universe

Details Relative information entropy of an inhomogeneous universe Relative information entropy of an inhomogeneous universe

2010-11-25

arxiv.org/abs/1011.5604v1

AIP Conf.Proc.1241:1074-1082, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, 4 figures, LaTeX 2e using aipproc.cls, published in AIP Conf. Proc., minor corrections made

Scientific paper

10.1063/1.3462602

In the context of averaging an inhomogeneous cosmological model, we propose a natural measure identical to the Kullback-Leibler relative information entropy, which expresses the distinguishability of the local inhomogeneous density field from its spatial average on arbitrary compact domains. This measure is expected to be an increasing function in time and thus to play a significant role in studying gravitational entropy. To verify this conjecture, we explore the time evolution of the measure using the linear perturbation theory of a spatially flat FLRW model and a spherically symmetric nonlinear solution. We discuss the generality and conditions for the time-increasing nature of the measure, and also the connection to the backreaction effect caused by inhomogeneities.

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