Einstein static universe and its stability in generalized Rastall gravity

The Einstein static (ES) state is a good candidate for describing the very early universe in terms of regular cosmological model which Big Bang singularity avoided. In present study we propose an ES solution framework generalized Rastall gravity (GRG), modified version original theory coupling parameter allowed to vary with respect spacetime coordinates. Introducing ansatz parameter, existence and corresponding stability solutions are investigated. We show that GRG capable stable singularity-free universe. problem transition from inflationary also addressed. find time variation equation values lying range |w|<1/3 value w=-1/3 can give rise such phase transition. vector tensor perturbations around studied, as well. case GRG, remain frozen, nevertheless, tenor grow way remains provided ratio gravitational constant Einsteinian one always exceeds minimum each mode.