# Nonminimal couplings, gravitational waves, and torsion in Horndeski's theory

## TL;DR

This paper extends Horndeski's gravity theory by incorporating torsion, revealing new torsional modes that could be detected through gravitational waves, thus broadening the phenomenological implications of scalar-tensor theories.

## Contribution

It introduces a framework to include and analyze torsion within Horndeski's theory using Cartan's formalism, highlighting the role of nonminimal couplings and derivatives in generating torsion.

## Key findings

- Torsion can be generated by nonminimal couplings in the Lagrangian.
- Metric perturbations couple to background torsion, producing detectable torsional modes.
- Torsional modes may be observed via gravitational waves, but not through gauge bosons.

## Abstract

The Horndeski Lagrangian brings together all possible interactions between gravity and a scalar field that yield second-order field equations in four-dimensional spacetime. As originally proposed, it only addresses phenomenology without torsion, which is a non-Riemannian feature of geometry. Since torsion can potentially affect interesting phenomena such as gravitational waves and early Universe inflation, in this paper we allow torsion to exist and propagate within the Horndeski framework. To achieve this goal, we cast the Horndeski Lagrangian in Cartan's first-order formalism, and introduce wave operators designed to act covariantly on p-form fields that carry Lorentz indices. We find that nonminimal couplings and second-order derivatives of the scalar field in the Lagrangian are indeed generic sources of torsion. Metric perturbations couple to the background torsion and new torsional modes appear. These may be detected via gravitational waves but not through Yang-Mills gauge bosons.