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

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.