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

TL;DR

This paper derives the post-Newtonian limit of a broad class of scalar-nonmetricity gravity theories, identifying conditions under which they mimic general relativity or deviate from it in solar system tests.

Contribution

It provides a comprehensive calculation of the post-Newtonian limit for generalized scalar-nonmetricity theories, revealing when they are indistinguishable from or differ from general relativity.

Findings

Many subclasses match general relativity at the post-Newtonian level.

Deviations from GR occur only with specific scalar-nonmetricity couplings.

Most theories in this class are consistent with solar system observations.

Abstract

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.