Coupling Metric-Affine Gravity to the Standard Model and Dark Matter Fermions

TL;DR

This paper explores how different formulations of metric-affine gravity, when coupled with the Standard Model and dark matter fermions, lead to observable differences, especially in dark matter production mechanisms.

Contribution

It constructs a generic coupled model of matter and gravity in metric-affine frameworks and identifies potential observable distinctions from other GR formulations.

Findings

Dark matter fermions can be produced via gravitational mechanisms unique to metric-affine gravity.

New interaction terms emerge in the equivalent metric theory when matter couples to different gravity formulations.

Observable differences in predictions can help distinguish between metric, Palatini, Einstein-Cartan, and Weyl gravity.

Abstract

General Relativity (GR) exists in different formulations, which are equivalent in pure gravity. Once matter is included, however, observable predictions generically depend on the version of GR. In order to quantify the resulting ambiguity, we employ metric-affine gravity, which encompasses as special cases the metric, Palatini, Einstein-Cartan and Weyl formulations. We first discuss the interaction of fermions with torsion and non-metricity, also commenting on projective symmetry. With a view towards the Standard Model, we then construct a generic model of (complex) scalar, fermionic and gauge fields coupled to GR and derive an equivalent metric theory, which features numerous new interaction terms. As a first observable consequence, we point out that a gravitational mechanism for producing dark matter in the form of singlet fermions can be used to distinguish between metric gravity and other formulations of GR.