(In)equivalence of Metric-Affine and Metric Effective Field Theories

TL;DR

This paper develops a comprehensive framework for metric-affine gravity theories, exploring their dynamical properties, phenomenological implications, and the emergence of the equivalence principle at low energies.

Contribution

It constructs the most general metric-affine effective field theories with matter, analyzing dynamical features and phenomenology, including pseudoscalar fields and emergent equivalence principle.

Findings

Identification of the most general metric-affine effective field theories.

Analysis of dynamical pseudoscalars from the Holst invariant.

Demonstration of the emergence of the equivalence principle at low energies.

Abstract

In a geometrical approach to gravity the metric and the (gravitational) connection can be independent and one deals with metric-affine theories. We construct the most general action of metric-affine effective field theories, including a generic matter sector, where the connection does not carry additional dynamical fields. Among other things, this helps in identifying the complement set of effective field theories where there are other dynamical fields, which can have an interesting phenomenology. Within the latter set, we study in detail a vast class where the Holst invariant (the contraction of the curvature with the Levi-Civita antisymmetric tensor) is a dynamical pseudoscalar. In the Einstein-Cartan case (where the connection is metric compatible and fermions can be introduced) we also comment on the possible phenomenological role of dynamical dark photons from torsion and compute interactions of the above-mentioned pseudoscalar with a generic matter sector and the metric. Finally, we show that in an arbitrary realistic metric-affine theory featuring a generic matter sector the equivalence principle always emerges at low energies without the need to postulate it.