Stability of the Einstein static universe in the presence of vacuum energy

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 the 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 center equilibrium point, which is cyclically stable. This allows nonsingular emergent cosmological models to be constructed in which initially the Universe oscillates indefinitely about an initial Einstein static solution and is thus past eternal.

Figure 1

The scale factor as a function of time (left) and a typical trajectory in the phase space $(a,\dot{a})$ (right).

Figure 2

The time dependence of ${\rho }_{\mathrm{rm}}{a}^4$ (left) and ${\rho }_{\Lambda }$ (right).