Stability of the flat FLRW metric in $f(T)$ gravity

Abstract

In this paper, we investigate the stability of the flat FLRW metric in $f(T)$ gravity. This is achieved by analysing the small perturbations, $\delta$ about the Hubble parameter and the matter energy density, ${\delta }_{\text{m}}$. We find that $\delta \propto \dot{H}/H$ and ${\delta }_{\text{m}}\propto H$. 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 $f(T)=\alpha T_0\left(1-\exp \left[-p\sqrt{\frac{T}{T_0}}\right]\right)$, 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 ${\delta }_{\text{m}}$, meaning that the matter perturbations persist during late times.

14 pages, 14 figures

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