Equation of the Perfect Fluid in the FRW Universe

TL;DR

This paper investigates the equation of state of perfect fluids in various gravity theories and dimensions within the FRW universe, revealing how gravity type and dimensionality influence critical points and phase transitions.

Contribution

It provides a comparative analysis of the perfect fluid equation of state across Einstein, Gauss-Bonnet, and Lovelock gravities in different dimensions, highlighting conditions for critical points and phase transitions.

Findings

No critical point in Einstein gravity in general

Critical points appear in Gauss-Bonnet gravity for dimensions 5-8

Phase transitions occur above the critical temperature when a critical point exists

Abstract

In this paper, we study the equation of state and its properties of the perfect fluid in the $D$-dimensional FRW universe under Einstein gravity, Gauss-Bonnet gravity and Lovelock gravity. In Einstein gravity, we get the equation of state and find that it has no critical point in the $P$-$V$ diagram, but its isothermal lines have minima in the $4$-dimensional case and are always negative in higher dimensions. In Gauss-Bonnet gravity, we get the equation of state and find that it has a critical point in the $5,6,7,8$-dimensional cases with phase transitions above the critical temperature. In Lovelock gravity, we get the equation of state and conditions of the critical points. Our work shows that both the theories of gravity and the dimensions of the FRW universe affect the existence of the critical point of the perfect fluid. Interestingly, if the critical point exists, phase transition always occures above the critical temperature.