We investigate whether or not an Einstein Static universe is a solution to
the cosmological equations in f(R) gravity. It is found that only one class
of f(R) theories admits an Einstein Static model, and that this class is
neutrally stable with respect to vector and tensor perturbations for all
equations of state on all scales. Scalar perturbations are only stable on all
scales if the matter fluid equation of state satisfies
cs2>65−1≈0.21. This result is remarkably similar to
the GR case, where it was found that the Einstein Static model is stable for
cs2>1/5.Comment: Minor changes, To appear in PR