Covariant Galileon

TL;DR

This paper investigates covariant galileon theories, demonstrating how a specific nonminimal coupling to curvature can produce second-order field equations while breaking the original Galilean invariance.

Contribution

It introduces a unique nonminimal coupling that ensures second-order equations in covariant galileon models, eliminating higher derivatives without adding degrees of freedom.

Findings

Nonminimal coupling removes higher derivatives from field equations

Second-order equations achieved in covariant galileon models

Original Galilean invariance is broken by the new coupling

Abstract

We consider the recently introduced "galileon" field in a dynamical spacetime. When the galileon is assumed to be minimally coupled to the metric, we underline that both field equations of the galileon and the metric involve up to third-order derivatives. We show that a unique nonminimal coupling of the galileon to curvature eliminates all higher derivatives in all field equations, hence yielding second-order equations, without any extra propagating degree of freedom. The resulting theory breaks the generalized "Galilean" invariance of the original model.