Exceptional scalar theories in de Sitter space

TL;DR

This paper explores the extension of special galileon and DBI scalar theories to de Sitter space, providing new formulations, field redefinitions, and symmetry interpretations that generalize flat space properties.

Contribution

It introduces a compact Lagrangian for the special galileon in de Sitter space and relates it to flat space dualities, also analyzing the DBI theory's formulations and symmetries in curved space.

Findings

New compact expression for the special galileon Lagrangian in de Sitter space

Field redefinition relating curved space galileon to flat space duality

Evidence that brane and dilaton formulations of DBI are related by a field redefinition

Abstract

The special galileon and Dirac-Born-Infeld (DBI) theories are effective field theories of a single scalar field that have many interesting properties in flat space. These theories can be extended to all maximally symmetric spaces, where their algebras of shift symmetries are simple. We study aspects of the curved space versions of these theories: for the special galileon, we find a new compact expression for its Lagrangian in de Sitter space and a field redefinition that relates it to the previous, more complicated formulation. This field redefinition reduces to the well-studied galileon duality redefinition in the flat space limit. For the DBI theory in de Sitter space, we discuss the brane and dilaton formulations of the theory and present strong evidence that these are related by a field redefinition. We also give an interpretation of the symmetries of these theories in terms of broken diffeomorphisms of de Sitter space.