Thermodynamics of $f(R)$ Theories of Gravity

TL;DR

This paper explores the thermodynamics of $f(R)$ gravity theories by linking Einstein frame scalar potentials to Jordan frame $f(R)$ functions, providing insights into stability and evolution.

Contribution

It introduces a novel approach by deriving $f(R)$ functions from Einstein frame potentials and analyzing their thermodynamical properties.

Findings

Thermodynamical interpretation of $f(R)$ gravity models.

Insights into (meta)stability of modified gravity theories.

Connection between Einstein frame potentials and Jordan frame functions.

Abstract

This paper starts from a toy model for inflation in a class of modified theories of gravity in the metric formalism. Instead of the standard procedure -- assuming a non-linear Lagrangian $f(R)$ in the Jordan frame -- we start from a simple $\phi^2$ potential in the Einstein frame and investigate the corresponding $f(R)$ in the former picture. The addition of an ad-hoc Cosmological Constant in the Einstein frame leads to a Thermodynamical interpretation of this physical system, which allows further insight on its (meta)stability and evolution.