Thermodynamics of $f(R)$ Gravity: The Double Well Potential Case

TL;DR

This paper explores the thermodynamic properties of $f(R)$ gravity with a double-well potential, deriving phase transition characteristics and critical phenomena in the context of gravitational theories.

Contribution

It extends the thermodynamics analogy to $f(R)$ gravity with a double-well potential, providing a parametric form of $f(R)$ and analyzing phase transitions and critical behavior.

Findings

Derived a parametric form of $f(R)$ in the Jordan frame.

Identified phase transition points and critical quantities.

Analyzed entropy jumps and specific-heat divergence.

Abstract

In this work we further extend the analysis of $f(R)$ theories of gravity in the metric formalism under the approach of a Thermodynamics analogy, proposed in arXiv:1911.04830v3. Here we assume a double-well inflationary potential in the Einstein frame and obtain a parametric form of $f(R)$ in the corresponding Jordan frame. The whole Thermodynamics picture then follows: an equation of state, binodal and spinodal curves, phase transition, critical quantities (pressure, volume and temperature), entropy jumps, specific-heat divergence (and the corresponding critical exponent) and a butterfly catastrophe.