Generalized second law of thermodynamics in f(T) gravity

TL;DR

This paper examines the generalized second law of thermodynamics within f(T) gravity models, analyzing their viability and the conditions under which the law holds or is violated in a cosmological context.

Contribution

It evaluates the GSL in two specific f(T) models, assesses their physical viability, and identifies conditions leading to GSL violation in the future.

Findings

GSL holds from early times to present in both models

Future GSL violation occurs for specific torsion scalar ranges

Models exhibit sudden future singularities

Abstract

We investigate the validity of the generalized second law (GSL) of gravitational thermodynamics in the framework of f(T) modified teleparallel gravity. We consider a spatially flat FRW universe containing only the pressureless matter. The boundary of the universe is assumed to be enclosed by the Hubble horizon. For two viable f(T) models containing $f(T)=T+\mu_1{(-T)}^n$ and $f(T)=T-\mu_2 T(1-e^{\beta\frac{T_0}{T}})$, we first calculate the effective equation of state and deceleration parameters. Then, we investigate the null and strong energy conditions and conclude that a sudden future singularity appears in both models. Furthermore, using a cosmographic analysis we check the viability of two models. Finally, we examine the validity of the GSL and find that for both models it is satisfied from the early times to the present epoch. But in the future, the GSL is violated for the special ranges of the torsion scalar T.