The generalized second law of thermodynamics in f(R) gravity for various choices of scale factor

TL;DR

This paper investigates the validity of the generalized second law of thermodynamics in f(R) gravity across different universe expansion scenarios and horizons, finding it always holds true.

Contribution

It demonstrates the universal validity of the GSL in f(R) gravity for various scale factors and horizons, using a specific functional form of f(R).

Findings

GSL holds for all considered scenarios.

Total entropy derivative remains positive over time.

Validity is independent of scale factor and horizon choice.

Abstract

The present study is aimed at investigating the validity of the generalized second law (GSL) of thermodynamics in $f(\cal R)$ gravity. Choosing $f(\cal R)=R+\xi R^{\mu}+\zeta R^{-\nu}$ [following Phys Rev D, 68, 123512 (2003)] we have computed the time derivatives of total entropy for various choices of scale factor pertaining to emergent, intermediate and logamediate scenarios of the universe. We have taken into account the radii of hubble, apparent, particle and event horizons while computing the time derivatives of entropy under various situations being considered. After analyzing through the plots of time derivative of total entropy against cosmic time it is observed that the derivative always stays at positive level that indicate the validity of GSL of thermodynamics in the $f(\cal R)$ gravity irrespective of the choices of scale factor and enveloping horizon.