Bi-galileon theory I: motivation and formulation

TL;DR

This work generalizes the galileon idea to a two-field bi-galileon theory, motivated by infrared modifications of gravity in co-dimension two braneworlds and exemplified by cascading cosmology. It provides a principled construction of the most general bi-galileon Lagrangian under Galilean invariance, identifies the decoupling-limit behavior where two scalar degrees of freedom govern deviations from GR, and introduces the action polynomial as a geometric tool to study maximally symmetric vacua and their stability. The framework clarifies how cascaded brane models realize bi-galileon dynamics, and shows that only one combination of scalars couples directly to matter, with a covariant completion discussed for consistency. Together with a companion phenomenology paper, this work establishes a tractable, ghost-free platform for exploring infrared gravity modifications and their cosmological consequences, while also permitting generalization to more galileon fields.

Abstract

We introduce bi-galileon theory, the generalisation of the single galileon model introduced by Nicolis et al. The theory contains two coupled scalar fields and is described by a Lagrangian that is invariant under Galilean shifts in those fields. This paper is the first of two, and focuses on the motivation and formulation of the theory. We show that the boundary effective theory of the cascading cosmology model corresponds to a bi-galileon theory in the decoupling limit, and argue that this is to be expected for co-dimension 2 braneworld models exhibiting infra-red modification of gravity. We then generalise this, by constructing the most general bi-galileon Lagrangian. By coupling one of the galileons to the energy-momentum tensor, we pitch this as a modified gravity theory in which the modifications to General Relativity are encoded in the dynamics of the two galileons. We initiate a study of phenomenology by looking at maximally symmetric vacua and their stability, developing elegant geometric techniques that trivially explain why some of the vacua have to be unstable in certain cases (eg DGP). A detailed study of phenomenology appears in our companion paper.