Study of Thermodynamic Quantities in Generalized Gravity Theories

TL;DR

This paper investigates thermodynamic properties like temperature, heat capacity, and sound speed in various generalized gravity theories, revealing consistent behaviors across models and universe geometries.

Contribution

It provides a comparative analysis of thermodynamic quantities in Brans-Dicke, Hořava-Lifshitz, and $f(R)$ gravities considering different universe models and matter contents.

Findings

Temperature and heat capacity decrease with universe expansion.

Squared speed of sound increases in Brans-Dicke and $f(R)$ theories.

Squared speed of sound varies in Hořava-Lifshitz gravity depending on universe curvature.

Abstract

In this work, we have studied the thermodynamic quantities like temperature of the universe, heat capacity and squared speed of sound in generalized gravity theories like Brans-Dicke, Ho$\check{\text r}$ava-Lifshitz and $f(R)$ gravities. We have considered the universe filled with dark matter and dark energy. Also we have considered the equation of state parameters for open, closed and flat models. We have observed that in all cases the equation of state behaves like quintessence. The temperature and heat capacity of the universe are found to decrease with the expansion of the universe in all cases. In Brans-Dicke and $f(R)$ gravity theories the squared speed of sound is found to exhibit increasing behavior for open, closed and flat models and in Ho$\check{\text r}$ava-Lifshitz gravity theory it is found to exhibit decreasing behavior for open and closed models with the evolution of the universe. However, for flat universe, the squared speed of sound remains constant in Ho$\check{\text r}$ava-Lifshitz gravity.