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

By rescaling the Gauss-Bonnet (GB) coupling constant $\alpha \rightarrow \alpha/(D-4)$andconsideringthe$D \rightarrow 4$ 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 $4D$ 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.