A formal introduction to Horndeski and Galileon theories and their generalizations

TL;DR

This paper reviews the mathematical foundations and various constructions of Horndeski and Galileon theories, including their generalizations, in both flat and curved spacetime, for single and multi-field models.

Contribution

It provides a comprehensive formal mathematical overview of Galileon and Horndeski theories and introduces their generalizations across different spacetime geometries.

Findings

Detailed classification of Galileon constructions in flat and curved space

Analysis of multi-field Galileon models and their properties

Discussion of the mathematical consistency and generalizations of these theories

Abstract

We review different constructions of Galileon theories in both flat and curved space, and for both single scalar field models as well as multi-field models. Our main emphasis is on the formal mathematical properties of these theories and their construction.