A metric-affine version of the Horndeski theory

TL;DR

This paper explores metric-affine scalar-tensor theories related to Horndeski models, showing how the connection can be integrated out to produce an equivalent metric theory with potential phenomenological implications.

Contribution

It introduces a metric-affine extension of Horndeski theories where the connection is algebraically eliminable, leading to an effective metric theory with additional K-essence features.

Findings

Connection describes a scalar-tensor Weyl geometry.

Equivalent metric theory includes an extra K-essence term.

The approach offers potential phenomenological applications.

Abstract

We study the metric-affine versions of scalar-tensor theories whose connection enters the action only algebraically. We show that the connection can be integrated out in this case, resulting in an equivalent metric theory. Specifically, we consider the metric-affine generalisations of the subset of the Horndeski theory whose action is linear in second derivatives of the scalar field. We determine the connection and find that it can describe a scalar-tensor Weyl geometry without a Riemannian frame. Still, as this connection enters the action algebraically, the theory admits the dynamically equivalent (pseudo)-Riemannian formulation in the form of an effective metric theory with an extra K-essence term. This may have interesting phenomenological applications.