Clausius relation and Friedmann equation in FRW universe model

Journal Article · Sat May 01 04:00:00 EDT 2010 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2010/05/030· OSTI ID:22272892

Cao, Qiao-Jun; Chen, Yi-Xin; Shao, Kai-Nan ^[1]

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1. Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027 (China)

It has been shown that Friedmann equation of FRW universe can be derived from the first law of thermodynamics in Einstein gravity, Gauss-Bonnet gravity, Lovelock gravity, scalar-tensor gravity and f(R) gravity. Moreover, it was pointed out that the temperature of the apparent horizon can be obtained using the tunneling formalism for the corresponding observers defined by Kodama vector. In this article, we find that the energy flux through the apparent horizon can be determined by using the Kodama vector. This implies the fact that the Clausius relation and the first law of thermodynamics associated with the apparent horizon in FRW universe is relative to the Kodama observers. We illustrate the derivation of Friedmann equation, and also extend the study to the cases of Hořava-Lifshitz gravity and IR modified Hořava-Lifshitz gravity.

• OSTI ID: 22272892
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 05 Vol. 2010; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
ASTROPHYSICS
COSMOLOGY
FIELD EQUATIONS
GRAVITATION
SCALARS
THERMODYNAMICS
TUNNEL EFFECT
UNIVERSE
VECTORS