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Phys. Rev. Lett. 92, 141302 (2004) [4 pages]

Information Entropy in Cosmology

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Akio Hosoya1 *, Thomas Buchert2,1,3 †, and Masaaki Morita4,5 ‡
1Department of Physics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152-0033, Japan
2Theoretische Physik, Ludwig-Maximilians-Universität, Theresienstrasse 37, D-80333 München, Germany
3Department of Physics and Research Center for the Early Universe (RESCEU), School of Science, The University of Tokyo, Tokyo 113-0033, Japan
4Department of Physics, Ochanomizu University, Ohtsuka, Bunkyo-ku, Tokyo 112-8610, Japan
5Advanced Research Institute for Science and Engineering, Waseda University, Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan

Received 17 August 2003; published 9 April 2004

The effective evolution of an inhomogeneous cosmological model may be described in terms of spatially averaged variables. We point out that in this context, quite naturally, a measure arises which is identical to a fluid model of the Kullback-Leibler relative information entropy, expressing the distinguishability of the local inhomogeneous mass density field from its spatial average on arbitrary compact domains. We discuss the time evolution of “effective information” and explore some implications. We conjecture that the information content of the Universe—measured by relative information entropy of a cosmological model containing dust matter—is increasing.


©2004 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevLett.92.141302
DOI: 10.1103/PhysRevLett.92.141302
PACS: 98.80.–k, 04.40.–b, 89.70.+c

* Electronic address: ahosoya@th.phys.titech.ac.jp
† Electronic address: buchert@theorie.physik.uni- muenchen.de
‡ Electronic address: morita@okinawa-ct.ac.jp

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