Thermodynamics of $f(R)$ Theories

TL;DR

This paper reviews $f(R)$ theories of gravity, explores a non-standard approach to phase transitions using Catastrophe Theory, and introduces a novel thermodynamic interpretation of these modified gravity models.

Contribution

It presents a new thermodynamic perspective on $f(R)$ theories, linking phase transitions and catastrophe theory to gravitational modifications.

Findings

Establishes a thermodynamic framework for $f(R)$ theories

Connects phase transitions with gravitational modifications

Introduces a novel interpretation of $f(R)$ models

Abstract

This series of three lectures was presented at ``Escola de Cosmologia e Gravita\c{c}\~ao" \url{https://cosmosecontexto.org.br/ecg-inscricoes} and webcast at \url{https://shorturl.at/2ZSI7} -- in Portuguese, but slides in English. We will go through a brief review on $f(R)$ theories (in the metric approach) and the usual requirements for successful modifications of General Relativity. Then we will open a large parenthesis to talk about a non-standard approach to Phase Transitions: the Catastrophe Theory. Finally, we will connect the previous lectures to introduce a new Thermodynamic interpretation of $f(R)$ theories.