  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.
