Abstract

We consider the teleparallel equivalent of Lovelock gravity and its natural extension, where the action is given by an arbitrary function f(T-L1, T-L2, ..., T-Ln) of the torsion invariants T-Li, which contain higher order torsion terms, and derive its field equations. Then, we consider the special case of f(T-L1,T-L2) gravity and study a cosmological scenario by selecting a particular f(T-L1, T-L2), and derive the Friedmann equations. Also, we perform a dynamical systems analysis to extract information on the evolution of the cosmological model. Mainly, we find that the model has a very rich phenomenology and can describe the acceleration of the universe at late times.