  The Einstein static universe has played a central role in a number of
emergent scenarios recently put forward to deal with the singular origin of the
standard cosmological model. Here we study the existence and stability of the
Einstein static solution in presence of vacuum energy corresponding to
conformally-invariant fields. We show that the presence of vacuum energy
stabilizes this solution by changing it to a centre equilibrium point, which is
cyclically stable. This allows non-singular emergent cosmological models to be
constructed in which initially the universe oscillates indefinitely about an
initial Einstein static solution and is thus past eternal.
