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

TL;DR

This paper examines the validity of the generalized second law of thermodynamics within f(R)-gravity models, focusing on apparent horizons in a FRW universe during inflation and late acceleration, revealing conditions for its satisfaction.

Contribution

It analyzes the GSL in f(R)-gravity with a specific model during different cosmic epochs, highlighting when the law holds or fails.

Findings

GSL holds during late acceleration for the model.

GSL is conditionally valid during early inflation.

The validity depends on the matter's equation of state.

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 $f(R)=R-\alpha/R+\beta R^{2}$, 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 the matter. But in the late acceleration regime, the GSL is always respected.