Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-09-11
Phys.Lett.B688:101-109,2010
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
11 pages, 2 figures, version to appear in Physics Letters B, typos corrected
Scientific paper
10.1016/j.physletb.2010.03.070
We show that it is possible to obtain a picture of equilibrium thermodynamics on the apparent horizon in the expanding cosmological background for a wide class of modified gravity theories with the Lagrangian density $f(R, \phi, X)$, where $R$ is the Ricci scalar and $X$ is the kinetic energy of a scalar field $\phi$. This comes from a suitable definition of an energy momentum tensor of the "dark" component that respects to a local energy conservation in the Jordan frame. In this framework the horizon entropy $S$ corresponding to equilibrium thermodynamics is equal to a quarter of the horizon area $A$ in units of gravitational constant $G$, as in Einstein gravity. For a flat cosmological background with a decreasing Hubble parameter, $S$ globally increases with time, as it happens for viable $f(R)$ inflation and dark energy models. We also show that the equilibrium description in terms of the horizon entropy $S$ is convenient because it takes into account the contribution of both the horizon entropy $\hat{S}$ in non-equilibrium thermodynamics and an entropy production term.
Bamba Kazuharu
Geng Chao-Qiang
Tsujikawa Shinji
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