Exceptional scalar theories in de Sitter space

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.

Automated summary

This study examines certain aspects of the special galileon and DBI theories in curved space. For the special galileon theory, a new compact expression for its Lagrangian in de Sitter space is discovered, along with a field redefinition that relates it to the previous, more complex formulation. This field redefinition simplifies into the well-studied galileon duality redefinition in the flat space limit. For the DBI theory in de Sitter space, the brane and dilaton formulations are discussed and strong evidence is presented to suggest that they are related by a field redefinition. Additionally, an interpretation of the symmetries of these theories in terms of broken diffeomorphisms of de Sitter space is provided.