Post-Newtonian limit of generalized scalar-teleparallel theories of gravity

We propose a general class of scalar-teleparallel theories, which are based on a scalar field which is coupled to a flat connection with torsion and nonmetricity, and study its post -Newtonian limit using the parametrized post -Newtonian formalism. We find that among this class there are theories whose postNewtonian limit fully agrees with general relativity; for others only the parameters /3 and gamma deviate from their general relativity values /3 = gamma = 1, while all other parameters remain the same, thus preserving total momentum conservation, local Lorentz invariance and local position invariance; finally, we also find theories whose post -Newtonian limit is pathological. Our main result is a full classification of the proposed theories into these different cases. We apply our findings to a number of simpler classes of theories and show that for these a subset of the aforementioned cases can be found.