The generalized second law of gravitational thermodynamics on the apparent horizon in f(R)-gravity

Abstract

We investigate the generalized second law (GSL) of thermodynamics in the framework of f(R)-gravity. We consider a FRW universe filled only with ordinary matter enclosed by the dynamical apparent horizon with the Hawking temperature. For a viable modified gravity model as f(R)=R−α/R+βR2, we examine the validity of the GSL during the early-inflation and late-acceleration eras. Our results show that for the selected f(R)-gravity model minimally coupled with matter, the GSL in the early-inflation epoch is satisfied only for the special range of the equation-of-state parameter of matter. But in the late-acceleration regime, the GSL is always respected.