Equilibrium thermodynamics in modified gravitational theories
Abstract
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,ϕ,X), where R is the Ricci scalar and X is the kinetic energy of a scalar field ϕ. This comes from a suitable definition of an energymomentum 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 S' in nonequilibrium thermodynamics and an entropy production term.
 Publication:

Physics Letters B
 Pub Date:
 April 2010
 DOI:
 10.1016/j.physletb.2010.03.070
 arXiv:
 arXiv:0909.2159
 Bibcode:
 2010PhLB..688..101B
 Keywords:

 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 11 pages, 2 figures, version to appear in Physics Letters B, typos corrected