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Entropy 2013, 15(9), 3620-3639; doi:10.3390/e15093620

Gravitational Entropy and Inflation

1,*  and 2
1 Institute of theoretical astrophysics, University of Oslo, P. O. Box 1029 Blindern, Oslo N-0315, Norway 2 Oslo and Akershus University College of Applied Sciences, Faculty of Engineering, P. O. Box 4 St. Olavs plass, Oslo N-0130, Norway
* Author to whom correspondence should be addressed.
Received: 28 June 2013 / Revised: 16 July 2013 / Accepted: 30 August 2013 / Published: 4 September 2013
(This article belongs to the Special Issue Entropy and the Second Law of Thermodynamics)
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The main topic of this paper is a description of the generation of entropy at the end of the inflationary era. As a generalization of the present standard model of the Universe dominated by pressureless dust and a Lorentz invariant vacuum energy (LIVE), we first present a flat Friedmann universe model, where the dust is replaced with an ideal gas. It is shown that the pressure of the gas is inversely proportional to the fifth power of the scale factor and that the entropy in a comoving volume does not change during the expansion. We then review different measures of gravitational entropy related to the Weyl curvature conjecture and calculate the time evolution of two proposed measures of gravitational entropy in a LIVE-dominated Bianchi type I universe, and a Lemaitre-Bondi-Tolman universe with LIVE. Finally, we elaborate upon a model of energy transition from vacuum energy to radiation energy, that of Bonanno and Reuter, and calculate the time evolution of the entropies of vacuum energy and radiation energy. We also calculate the evolution of the maximal entropy according to some recipes and demonstrate how a gap between the maximal entropy and the actual entropy opens up at the end of the inflationary era.
Keywords: arrow of time; inflation; gravitational entropy arrow of time; inflation; gravitational entropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Elgarøy, Ø.; Grøn, Ø. Gravitational Entropy and Inflation. Entropy 2013, 15, 3620-3639.

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