Post-Newtonian limit of generalized symmetric teleparallel gravity

TL;DR

This paper investigates the post-Newtonian limit of generalized symmetric teleparallel gravity using the PPN formalism, identifying classes of theories consistent with observational constraints and analyzing their deviations from general relativity.

Contribution

It introduces a parameterized framework for symmetric teleparallel gravity and classifies theories based on their PPN parameters, showing some match GR and others can be tuned to do so.

Findings

Two families of theories match GR's PPN parameters.

Some theories can be tuned to approximate GR closely.

Others lack well-defined post-Newtonian solutions.

Abstract

In this article we analyze the post-Newtonian approximation of a generalization of the symmetric teleparallel gravity with the help of the parameterized post-Newtonian (PPN) formalism. This class of theories is based on a free function of the five independent quadratic contractions of the non-metricity tensor. By calculating the PPN metric of these theories, we can restrict the Taylor coefficients of the free function with the help of the PPN parameters and their observational bounds. We find two families of theories whose PPN parameters are identical to those of general relativity, and thus in full agreement with observations. For three further families, we find that only the PPN parameters $\beta$ and $\gamma$ deviate, but can be brought arbitrarily close to their general relativity values by an appropriate choice of the Lagrangian, so that also these families contain candidate theories which agree with observations. The remaining theories either possess no well-defined solution of the post-Newtonian field equations, or possess a post-Newtonian limit which exceeds the form assumed in the PPN formalism.