Bi-galileon theory I: motivation and formulation

TL;DR

This paper introduces the bi-galileon theory, a two-scalar-field extension of the galileon model, motivated by cascading cosmology and braneworld models, and explores its formulation, stability, and potential as a modified gravity theory.

Contribution

It formulates the most general bi-galileon Lagrangian, links it to cascading cosmology, and develops geometric techniques for analyzing vacua stability.

Findings

Boundary effective theory matches bi-galileon in decoupling limit

Constructed the most general bi-galileon Lagrangian

Identified stable and unstable vacua configurations

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.