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

TL;DR

This paper classifies a broad class of scalar-teleparallel gravity theories based on their post-Newtonian limits, identifying which align with general relativity and which deviate, thus informing their viability.

Contribution

It provides a comprehensive classification of scalar-teleparallel theories according to their post-Newtonian behavior, highlighting cases that match or deviate from general relativity.

Findings

Some theories fully agree with general relativity in the post-Newtonian limit.

Certain theories only alter parameters β and γ, maintaining other invariances.

A subset of theories exhibit pathological post-Newtonian behavior.

Abstract

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 post-Newtonian limit fully agrees with general relativity; for others only the parameters $\beta$ and $\gamma$ deviate from their general relativity values $\beta = \gamma = 1$, 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.