Post-Newtonian limit of scalar-torsion theories of gravity as analogue to scalar-curvature theories

We consider a recently proposed class of extended teleparallel theories of gravity, which entail a scalar field which is nonminimally coupled to the torsion of a flat, metric-compatible connection. This class of scalar-torsion theories of gravity is constructed in analogy to and as a direct extension of the well-studied class of scalar-curvature gravity theories, and has various common features, such as the conformal frame freedom. For this class we determine the parametrized post-Newtonian limit, both for a massive and for a massless scalar field. In the massive case, we determine the effective gravitational constant and the pos-tNewtonian parameter gamma, both of which depend on the distance between the gravitating and test masses. In the massless case, we calculate the full set of parameters and find that only gamma and beta potentially deviate from their general relativity values. In particular, we find that for a minimally coupled scalar field, the theory becomes indistinguishable from general relativity at this level of the post-Newtonian approximation.