The generalized second law of thermodynamics for interacting $f(R)$ gravity

TL;DR

This paper investigates the validity of the generalized second law of thermodynamics within interacting $f(R)$ gravity models in a flat FRW universe, demonstrating that entropy increases due to the interaction and providing exact solutions for specific models.

Contribution

It introduces a framework for analyzing the GSL in interacting $f(R)$ gravity and derives exact solutions for models with power-law curvature dependence.

Findings

Total entropy increases with interaction.

Exact solutions found for power-law $f(R)$ models.

Interaction affects the evolution of the universe's thermodynamics.

Abstract

We examine the validity of the generalized second law (GSL) of gravitational thermodynamics in the context of interacting $f(R)$ gravity. We take into account that the boundary of the universe to be confined by the dynamical apparent horizon in a flat FRW universe. We study the effective equation of state, deceleration parameter and GSL in this interaction-framework. We find that the evolution of the total entropy increases through the interaction term. As a example, we consider a $f(R)$ gravity with a power-law dependence on the curvature $R$. Here, we find exact solutions for a model in which the interaction term is related to the total energy density of matter.