Einstein Static Universe and its Stability in Generalized Rastall Gravity

TL;DR

This paper explores Einstein static universe solutions within generalized Rastall gravity, demonstrating conditions for stability and phase transition to inflation, with analysis of perturbations showing potential for a stable, singularity-free early universe model.

Contribution

It introduces a stable Einstein static universe solution in generalized Rastall gravity with variable coupling, analyzing its stability and transition to inflation.

Findings

GRG can describe a stable, singularity-free Einstein static universe.

A phase transition from static to inflationary state is possible via equation of state variation.

Tensor perturbations can grow while maintaining stability under certain conditions.

Abstract

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