Symmetries for Galileons and DBI scalars on curved space

TL;DR

This paper develops a broad class of four-dimensional effective field theories with curved space Galileons and DBI scalars, derived from gravitational actions for branes in higher dimensions, with potential cosmological applications.

Contribution

It constructs a general framework for curved space Galileons and DBI theories with nonlinear symmetries from higher-dimensional brane embeddings, extending flat space models.

Findings

Derived Galileon and DBI theories on de Sitter and anti-de Sitter spaces.

Identified symmetries that protect scalar potentials and masses.

Provided explicit examples from maximally symmetric brane embeddings.

Abstract

We introduce a general class of four-dimensional effective field theories which include curved space Galileons and DBI theories possessing nonlinear shift-like symmetries. These effective theories arise from purely gravitational actions for 3-branes probing higher dimensional spaces. In the simplest case of a Minkowski brane embedded in a higher dimensional Minkowski background, the resulting four-dimensional effective field theory is the Galileon one, with its associated Galilean symmetry and second order equations. However, much more general structures are possible. We construct the general theory and explicitly derive the examples obtained from embedding maximally symmetric branes in maximally symmetric ambient spaces. Among these are Galileons and DBI theories with second order equations that live on de Sitter or anti-de Sitter space, and yet retain the same number of symmetries as their flat space counterparts, symmetries which are highly non-trivial from the 4d point of view. These theories have a rich structure, containing potentials for the scalar fields, with masses protected by the symmetries. These models may prove relevant to the cosmology of both the early and late universe.