On the Stability of the Einstein Static Universe

TL;DR

This paper analyzes the stability of the Einstein static universe, showing it is neutrally stable under certain conditions against various perturbations, with implications for the universe's initial state and evolution.

Contribution

It provides a covariant analysis of the stability of the Einstein static universe, including effects of scalar fields and Bianchi modes, extending previous stability studies.

Findings

Stable against vector and tensor perturbations if c_s^2 > 1/5

Unstable if c_s^2 ≤ 1/5

Bianchi type IX modes destabilize the universe

Abstract

We show using covariant techniques that the Einstein static universe containing a perfect fluid is always neutrally stable against small inhomogeneous vector and tensor perturbations and neutrally stable against adiabatic scalar density inhomogeneities so long as c_{s}^2>1/5, and unstable otherwise. We also show that the stability is not significantly changed by the presence of a self-interacting scalar field source, but we find that spatially homogeneous Bianchi type IX modes destabilise an Einstein static universe. The implications of these results for the initial state of the universe and its pre-inflationary evolution are also discussed.