On the stability of Einstein static universe at background level in massive bigravity

TL;DR

This paper investigates the stability of Einstein static universe solutions within massive bigravity theory, revealing dependencies on spatial curvature and graviton mass, and identifying conditions for stability through dynamical analysis.

Contribution

It introduces new static universe solutions in massive bigravity and analyzes their stability, considering the effects of spatial curvature and graviton mass.

Findings

Stable solutions exist for certain ranges of equation of state parameters.

Stability depends on the spatial curvature and graviton mass.

Solutions are viable for hierarchies where graviton mass is much less than Planck mass.

Abstract

We study the static cosmological solutions and their stability at background level in the framework of massive bigravity theory with Friedmann-Robertson-Walker (FRW) metrics. By the modification proposed in the cosmological equations subject to a perfect fluid we obtain new solutions interpreted as the Einstein static universe. It turns out that the non-vanishing size of initial scale factor of Einstein static universe depends on the non-vanishing three-dimensional spatial curvature of FRW metrics and also the graviton's mass. By dynamical system approach and numerical analysis, we find that the extracted solutions for closed and open universes can be stable for some viable ranges of equation of state parameter, viable values of fraction of two scale factors, and viable values of graviton's mass obeying the hierarchy $m << M_Pl$ which is more cosmologically motivated.