Teleparallel equivalent of Lovelock gravity, generalizations and cosmological applications

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.