Effective Pressure of the FRW Universe

TL;DR

This paper investigates the effective pressure in N-dimensional FRW universes across Einstein, Gauss-Bonnet, and Lovelock gravities, revealing its properties and relations to ordinary pressure under specific conditions.

Contribution

It introduces a unified definition of effective pressure in various gravity theories and analyzes its behavior across different dimensions and parameters.

Findings

Effective pressure in Einstein gravity is always negative and decreases with horizon radius.

In Gauss-Bonnet gravity, effective pressure depends on the coupling constant and dimension.

Lovelock gravity allows for multiple zero and extremum points of effective pressure.

Abstract

In this paper, we study the effective pressure of the $N$-dimensional FRW(Friedmann-Robertson-Walker) universe in Einstein gravity, Gauss-Bonnet gravity, and Lovelock gravity. The effective pressure is defined by $P_{eff}:=-d E/d V$, where $E=\rho V$ is the effective energy and $V$ is the volume of the FRW universe inside the apparent horizon. The effective pressure in Einstein gravity is always negative and its absolute value decreases with the horizon radius $R_A$. The effective pressure in Gauss-Bonnet gravity is different with the one in Einstein gravity only when $N\geq6$. In this case, if $\alpha>0$, the effective pressure is always negative, but if $\alpha<0$, it is not always negative and has a minimum. The effective pressure in Lovelock gravity can have multiple zero-points and extreme points. The effective pressure in different dimensions has interesting relations. We also find that under certain condition, the effective pressure is equivalent with the `ordinary' pressure $p$ of the perfect fluid, and this condition do not depend on the specific choice of gravitational theories.