The P-V Phase Transition of the FRW Universe

TL;DR

This paper explores the thermodynamic properties of the FRW universe, defining pressure via work density and analyzing phase transitions in Einstein and modified gravity frameworks, revealing a phase transition only in the latter.

Contribution

It introduces a novel thermodynamic framework for the FRW universe and identifies a P-V phase transition in modified gravity not present in Einstein gravity.

Findings

No P-V phase transition in Einstein gravity

Presence of P-V phase transition in modified gravity

Critical exponents match mean field theory

Abstract

We define thermodynamic pressure $P$ by work density $W$ as the conjugate quantity of thermodynamic volume $V$ from field equation. We derive the equations of state $P$=$P(V, T)$ for the Friedmann-Robertson-Walker (FRW) universe in Einstein gravity and a modified gravity respectively. We find that the equation of state from Einstein gravity shows no $P$-$V$ phase transition, while the equation of state from the modified gravity does, where the critical exponents are the same as those in mean field theory.