The stability of the Einstein static state in $f(T)$ gravity

TL;DR

This paper investigates the stability of the Einstein static universe within $f(T)$ gravity, showing that modifications to gravity can stabilize these solutions in both open and closed spatial geometries, unlike in general relativity.

Contribution

It demonstrates that $f(T)$ gravity allows stable Einstein static solutions in cases where general relativity does not, expanding the conditions for stability.

Findings

Stable Einstein static solutions exist in both open and closed $f(T)$ universes.

In closed universes, stability requires $w<1/3$, broader than in GR.

Open universe solutions are stable in $f(T)$ but not in GR.

Abstract

The stability of the Einstein static universe against the homogeneous scalar perturbations in $f(T)$ gravity is analyzed. Both the spatial closed and open universes are considered. We find that the stable Einstein static solutions exist in both cases. Considering a concrete $f(T)$ model and assuming that the cosmic energy has a constant equation of state $w$, we obtain that, in the closed case, $w<1/3$ is required. Thus, $f(T)$ theory gives a larger region of $w$ than that in general relativity ($-1<w<-1/3$) to have the stable Einstein static solution. For the open universe, $f(T)$ theory allows the stable Einstein static solution, although this kind of solution is forbidden in general relativity. Thus, a modification of gravity can play a crucial role in stabilizing the Einstein static solution.