Induced Matter Brane Gravity and Einstein Static Universe

TL;DR

This paper examines the stability of the Einstein static universe within induced matter brane gravity, revealing conditions for stability against various perturbations and highlighting differences from classical general relativity.

Contribution

It demonstrates the existence of a stable Einstein static universe in induced matter brane gravity, contrasting with classical GR, and identifies specific stability conditions for perturbations.

Findings

Stable against scalar perturbations with specific equation of state variation

Neutral stability against vector perturbations

Guaranteed stability against tensor perturbations due to positive spatial curvature

Abstract

We investigate stability of the Einstein static universe against the scalar, vector and tensor perturbations in the context of induced matter brane gravity. It is shown that in the framework of this model, the Einstein static universe has a positive spatial curvature. In contrast to the classical general relativity, it is found that a stable Einstein static universe against the scalar perturbations does exist provided that the variation of time dependent geometrical equation of state parameter is proportional to the minus of the variation of the scale factor, $\delta \omega_{g}(t)=-C\delta a(t)$. We obtain neutral stability against the vector perturbations, and the stability against the tensor perturbations is guaranteed due to the positivity of the spatial curvature of the Einstein static universe in induced matter brane gravity.