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 $f(T_{{L_1}}, T{{L_2}},\cdot \cdot \cdot , T{{L_n}})$ofthetorsioninvariants$T{_{L_i}}$, which contain higher order torsion terms, and derive its field equations. Then, we consider the special case of $f(T_{{}_{L_1}},T_{{}_{L_2}})$ gravity and study a cosmological scenario by selecting a particular $f(T_{{}_{L_1}},T_{{}_{L_2}})$, 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