Equation of the Perfect Fluid in the FRW Universe

TL;DR

The paper investigates van der Waals–like thermodynamics of a perfect fluid in the D-dimensional FRW universe under Einstein, Gauss–Bonnet, and Lovelock gravities. By deriving the equation of state in each theory and analyzing the presence of critical points in the P–V (or equivalent) plane, it shows that critical phenomena and phase transitions depend sensitively on both the gravitational theory and the spacetime dimension. In Einstein gravity, no critical point occurs; in Gauss–Bonnet gravity, critical points and above-Tc phase transitions appear for certain dimensions with negative coupling, and Lovelock gravity yields general criticality conditions. The results reveal a robust link between gravitational dynamics and the thermodynamic behavior of cosmological fluids, with phase transitions consistently occurring above Tc 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.

Figures (7)

• Figure 1: Isothermal lines of perfect fluid in the (3+1)-dimensional FRW universe under Einstein gravity.
• Figure 2: Isothermal lines of the perfect fluid in the (4+1)-dimensional FRW universe under Einstein gravity.
• Figure 3: Isothermal lines of the perfect fluid in the (5+1)-dimensional FRW universe under Einstein gravity.
• Figure 4: Isothermal lines of the perfect fluid in (4+1)-dimensional FRW universe under Gauss-Bonnet gravity with $\tilde{\alpha}=-1$.
• Figure 5: Isothermal lines of the (5+1)-dimensional FRW universe in Gauss-Bonnet gravity with $\tilde{\alpha}=-1$.