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

TL;DR

This paper introduces a new class of galilean invariant models coupled with a dynamical metric, extending massive gravity theories while maintaining second order equations and symmetries, and explores their unique interactions.

Contribution

It proposes a covariant master theory coupling galileons to a massive graviton, achieving all key properties simultaneously and extending ghost-free massive gravity with novel galileon interactions.

Findings

New galileon interactions with the graviton's longitudinal mode

Models maintain second order equations and galilean symmetry

Interactions are ghost-free despite higher order terms

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.