Dynamical systems approach and generic properties of f(T) cosmology

We present a systematic analysis of the dynamics of flat Friedmann-LemaCEtre-Robertson-Walker cosmological models with radiation and dust matter in generalized teleparallel f(T) gravity. We show that the cosmological dynamics of this model are fully described by a function W(H) of the Hubble parameter, which is constructed from the function f(T). After reducing the phase space to two dimensions, we derive the conditions on W(H) for the occurrence of de Sitter fixed points, accelerated expansion, crossing the phantom divide, and finite time singularities. Depending on the model parameters, it is possible to have a bounce (from contraction to expansion) or a turnaround (from expansion to contraction), but cyclic or oscillating scenarios are prohibited. As an illustration of the formalism we consider power law f(T) = T + alpha(-T)(n) models, and show that these allow only one period of acceleration and no phantom divide crossing.