A Covariant Master Theory for Novel Galilean Invariant Models and Massive Gravity

TL;DR

This work constructs a covariant framework that couples a multiplet of galileon scalars $\pi^I$ to a dynamical massive graviton by embedding a brane in a higher-dimensional bulk and introducing a dynamical world-volume metric. Ghost-free interactions are achieved by combining a ghost-free dRGT-like mixing between $g_{\mu\nu}$ and the induced metric $\bar{g}_{\mu\nu}$ with DBI/Lovelock terms for $\bar{g}_{\mu\nu}$, while maintaining galileon-like shift symmetries. In the flat-bulk decoupling limit, new scalar–longitudinal graviton couplings arise, featuring higher-derivative terms that remain ghost-free due to degeneracy and constraint structure, as demonstrated by toy models and a Hamiltonian analysis. The construction provides a consistent platform to explore cosmological and gravitational phenomenology of galileon invariance in a fully dynamical gravity setting, with a clear path toward assessing stability beyond the decoupling limit. Although a complete nonperturbative ghost proof beyond the DLC is not delivered, the framework coherently extends ghost-free galileon and dRGT massive gravity theories and offers novel interactions for further study.

Abstract

Coupling the galileons to a curved background has been a tradeoff between maintaining second order equations of motion, maintaining the galilean shift symmetries, and allowing the background metric to be dynamical. We propose a construction which can achieve all three for a novel class of galilean invariant models, by coupling a scalar with the galilean symmetry to a massive graviton. This generalizes the brane construction for galileons, by adding to the brane a dynamical metric, (non-universally) interacting with the galileon field. Alternatively, it can be thought of as an extension of the ghost-free massive gravity, or as a massive graviton-galileon scalar-tensor theory. In the decoupling limit of these theories, new kinds of galileon invariant interactions arise between the scalar and the longitudinal mode of the graviton. These have higher order equations of motion and infinite powers of the field, yet are ghost-free.