  We consider alternative inflationary cosmologies in massive gravity with
degenerate reference metrics and study the feasibilities of the emergent
universe scenario, bouncing and cyclic universes. We focus on the construction
of the Einstein static universe, classes of exact solutions of bouncing and
cyclic universes in degenerate massive gravity. We further study the
stabilities of the Einstein static universe against both homogeneous and
inhomogeneous scalar perturbations and give the parameters region for a stable
Einstein static universe.
