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

Understand

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.