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Parametrized post-Newtonian limit of generalized scalar-nonmetricity theories of gravity

In this article we calculate the post-Newtonian limit of a general class of scalar-nonmetricity theories of gravity. The action is assumed to be a free function of the nonmetricity scalar, the kinetic term of the scalar field, two derivative couplings and the scalar field itself. We use the parametrized post-Newtonian formalism to solve the arising field equations for the case of a massless scalar field in order to compare several subclasses of this theory to solar system observations. In particular, we find several classes of theories which are indistinguishable from general relativity on the post-Newtonian level and therefore, should be studied further. Most remarkably, we find that this is the generic case, while a post-Newtonian limit that deviates from general relativity occurs only for a particular coupling between the scalar field and nonmetricity.