Stability of Einstein Static Universe over Lyra Geometry

The existence and stability conditions of Einstein static universe against homogeneous scalar perturbations in the context of Lyra geometry is investigated. The stability condition is obtained in terms of the constant equation of state parameter $\omega=p/\rho$ depending on energy density $\rho_0$ and scale factor $a_0$ of the initial Einstein static universe. Also, the stability against vector and tensor perturbations is studied. It is shown that a stable Einstein static universe can be found in the context of Lyra geometry against scalar, vector and tensor perturbations for suitable range and values of physical parameters.