Einstein static universe in the Rastall theory of gravity

We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of the Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy originating from conformally invariant fields is stable. Using the fix point method and taking linear homogeneous perturbations, we find that the scale factor of the Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the coupling parameter. between the energy-momentum tensor and the gradient of the Ricci scalar. Thus, in the present model and in the presence of vacuum energy, our universe can stay at the Einstein static state past-eternally, which means that the big bang singularity may be resolved successfully in the context of the Einstein static universe in the Rastall theory.