Phase space analysis of interacting dark energy in f(T) cosmology

In this paper, we examine the interacting dark energy model in $f(T)$ cosmology. We assume dark energy as a perfect fluid and choose a specific cosmologically viable form $f(T)= β\sqrt{T}$. We show that there is one attractor solution to the dynamical equation of $f(T)$ Friedmann equations. Further we investigate the stability in phase space for a general $f(T)$ model with two interacting fluids. By studying the local stability near the critical points, we show that the critical points lie on the sheet $u^*=(c-1)v^*$ in the phase space, spanned by coordinates $(u,v,Ω,T)$. From this critical sheet, we conclude that the coupling between the dark energy and matter $c\in (-2,0)$.

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