Stability of the Einstein Static Universe in $4 D$ Gauss-Bonnet Gravity

TL;DR

This paper explores the stability of the Einstein static universe within four-dimensional Gauss-Bonnet gravity, demonstrating conditions under which both closed and open universes remain stable against various perturbations.

Contribution

It introduces a novel analysis of the Einstein static universe stability in 4D Gauss-Bonnet gravity, considering both homogeneous and inhomogeneous scalar perturbations.

Findings

Both closed and open universes can be stable.

Stability holds against scalar perturbations.

The emergent universe scenario is feasible in 4D GB gravity.

Abstract

By rescaling the Gauss-Bonnet (GB) coupling constant $\alpha \rightarrow \alpha/(D-4)$ and considering the $D \rightarrow 4$ limit, the GB gravity gives rise to nontrivial modification of general relativity in four dimensions. In this work, we investigate the realization of the emergent universe scenario in the $4 D$ GB gravity. First, we obtain the Einstein static universe filled with a perfect fluid. Then, we show that both spatially closed and open universes can be stable against both homogeneous and inhomogeneous scalar perturbations simultaneously.