Einstein static universe in hybrid metric-Palatini gravity

Hybrid metric-Palatini gravity is a recent and novel approach to modified theories of gravity, which consists of adding to the metric Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. It was shown that the theory passes local tests even if the scalar field is very light, and thus implies the existence of a long-range scalar field, which is able to modify the dynamics in galactic and cosmological scales, but leaves the Solar System unaffected. In this work, motivated by the possibility that the Universe may have started out in an asymptotically Einstein static state in the inflationary universe context, we analyze the stability of the Einstein static universe by considering linear perturbations in the respective dynamically equivalent scalar-tensor representation of hybrid metric-Palatini gravity. Considering linear homogeneous and inhomogeneous perturbations, the stability regions of the Einstein static universe are parametrized by the first and second derivatives of the scalar potential, and it is explicitly shown that a large class of stable solutions exists in the respective parameter space, in the context of hybrid metric-Palatini gravity.