In this paper, we investigate the stability of the flat Friedmann-Lemaitre-Robertson-Walker metric in $f(T)$ gravity. This is achieved by analyzing the small perturbations, $\delta$ about the Hubble parameter and the matter energy density, ${\delta }_{\mathrm{m}}$. We find that $\delta \propto \dot{H}/H$ and ${\delta }_{\mathrm{m}}\propto H$. Since the Hubble parameter depends on the function $f(T)$, two models were considered (A) the power-law model $f(T)=\alpha (-T{)}^n$, and (B) the exponential model $f(T)=\alpha T_0(1-\exp [-p\sqrt{\frac{T}{T_0}}])$, where the parameters $n$ and $p$ were chosen to give comparable physical results. For the parameters considered, it was found that the solutions are stable with vanishing $\delta$ and decaying then constant ${\delta }_{\mathrm{m}}$, meaning that the matter perturbations persist during late times.

• Received 27 October 2016

DOI:https://doi.org/10.1103/PhysRevD.94.124054