Thermodynamics of FLRW universe in Quadratic Gravity

TL;DR

This paper explores the thermodynamic properties of quadratic gravity in a D-dimensional FLRW universe, deriving key quantities and analyzing phase transitions and stability conditions influenced by quadratic curvature terms.

Contribution

It introduces a comprehensive thermodynamic analysis of quadratic gravity in FLRW cosmology, including generalized energy, entropy, and phase transition criteria, highlighting differences from general relativity.

Findings

Quadratic terms alter thermodynamic stability conditions.

Identification of critical points for phase transitions.

New thermodynamic behaviors emerge compared to GR.

Abstract

In this paper, we investigate the thermodynamic aspects of quadratic gravity in a $D$-dimensional Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. First, we derive the field equations and the effective energy-momentum tensor for quadratic gravity. Then, using these equations, we obtain the generalized Misner-Sharp energy within the framework of this model. We consider the thermodynamic behavior of the apparent horizon and derive the equations of state related to the pressure, temperature, and radius of the apparent horizon. Using the thermodynamic pressure, we obtain the critical points corresponding to phase transitions. We determine the critical temperature and critical radius in terms of model parameters, including the quadratic coupling and the cosmological constant. We also examine key thermodynamic quantities, such as Wald entropy, specific heat at constant pressure, enthalpy, Gibbs free energy. By examining the behavior of these quantities, we can gain insight into the thermodynamic stability of the quadratic gravity model. In particular, we find that quadratic terms change the stability conditions and can lead to new thermodynamic behaviors compared to general relativity.