Thermodynamics of the FRW Universe at the Event Horizon in Palatini f(R) Gravity

A S Sefiedgar,M Mirzazadeh

doi:10.1155/2018/1250213

Abstract

In an accelerated expanding universe, one can expect the existence of an event horizon. It may be interesting to study the thermodynamics of the Friedmann-Robertson-Walker (FRW) universe at the event horizon. Considering the usual Hawking temperature, the first law of thermodynamics does not hold on the event horizon. To satisfy the first law of thermodynamics, it is necessary to redefine Hawking temperature. In this paper, using the redefinition of Hawking temperature and applying the first law of thermodynamics on the event horizon, the Friedmann equations are obtained in f(R) gravity from the viewpoint of Palatini formalism. In addition, the generalized second law (GSL) of thermodynamics, as a measure of the validity of the theory, is investigated.

Highlights

The existence of a deep connection between gravity and thermodynamics is one of the greatest discoveries in theoretical physics [1,2,3,4,5]
Applying the first law of thermodynamics on the event horizon and using the usual entropy-area relation, we have derived the Friedmann equations the same as the ones obtained via other approaches
The apparent horizon thermodynamics has been studied by many authors in FRW universe, the event horizon thermodynamics is not investigated enough

Summary

Introduction

The existence of a deep connection between gravity and thermodynamics is one of the greatest discoveries in theoretical physics [1,2,3,4,5]. Using the Chakraborty redefinition of Hawking temperature, Tu and Chen have considered a universe dominated by tachyon fluid and obtained a good thermodynamical description on the event horizon [27]. Tu and Chen have introduced a new redefinition of the temperature in a universe with an arbitrary spatial curvature [25] They have investigated the thermodynamics on the event horizon in metric f(R) gravity. We are going to apply Hawking temperature redefinition introduced by Tu and Chen in [25] to investigate the event horizon thermodynamics from the viewpoint of Palatini f(R) gravity. Applying the first law of thermodynamics on the event horizon and using the usual entropy-area relation, we have derived the Friedmann equations the same as the ones obtained via other approaches. The generalized second law of thermodynamics can be satisfied by choosing suitable f(R) functions

Hawking Temperature Redefinition on the Event Horizon

The Generalized Second Law of Thermodynamics

Conclusions