Covariant formulation of scalar-torsion gravity

We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, f (T, ), thus encompassing the cases of f (T) gravity and a nonminimally coupled scalar field as subclasses. The action is manifestly Lorentz invariant when besides the tetrad one allows for a flat but nontrivial spin connection. We derive the field equations and demonstrate how the antisymmetric part of the tetrad equations is automatically satisfied when the spin connection equation holds. The spin connection equation is a vital part of the covariant formulation, since it determines the spin connection associated with a given tetrad. We discuss how the spin connection equation can be solved in general and provide the cosmological and spherically symmetric examples. Finally, we generalize the theory to an arbitrary number of scalar fields.