Misner-Sharp Energy and P-V Criticality in Quasi-Topological Cosmology

TL;DR

This paper develops a thermodynamic framework for FRW universes in quasi-topology gravity, deriving the equation of state and revealing $P$-$V$ phase transitions with critical exponents, linking cosmology and phase transition theory.

Contribution

It introduces a consistent thermodynamic description for quasi-topology cosmology, including the Misner-Sharp energy and phase transition analysis, which is novel in this gravity context.

Findings

Misner-Sharp energy equals $ ho V$ inside the apparent horizon.

The universe exhibits $P$-$V$ phase transitions.

Critical exponents for the phase transition are calculated.

Abstract

We presented a sound foundation of thermodynamics for a Friedmann-Robertson-Walker (FRW) universe from the first principle in ground-breaking work [Hu et al., JHEP12 (2022) 168]. Based on such an approach, we explore the thermodynamics of cosmology in quasi-topology gravity. Starting from the unified first law, we first obtain the well-defined Misner-Sharp energy in quasi-topology cosmology. We demonstrate that the Misner-Sharp energy is equal to $\rho V$ inside the apparent horizon. Further, the unified first law requires extra terms for generalized force and conjugate generalized position, which are identified as thermodynamic pressure and thermodynamic volume, respectively. Hence we naturally derive the equation of state of the FRW universe in quasi-topology gravity, and show that it undergoes $P$-$V$ phase transitions. We calculate the critical exponents for the phase transition, which may be beneficial to probe the micro theory of quasi-topology gravity.