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

Stability of the Einstein static universe in presence of vacuum energy