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A formal introduction to Horndeski and Galileon theories and their generalizations

Cedric Deffayet, Daniele A Steer

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.

A formal introduction to Horndeski and Galileon theories and their generalizations

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.

Paper Structure

This paper contains 15 sections, 61 equations.

Table of Contents

  1. Flat space-time Galileons in arbitrary dimension
  2. Introduction: the canonical Galileon Lagrangian
  3. Field equations in $D$-dimensions
  4. Explicit expression for Galileons in $D=4$ dimensions, and some consequences
  5. Other form of Lagrangians
  6. Generalizing flat space-time Galileons
  7. Generalized single-field Galileons
  8. Multifield theories
  9. Covariant Galileons and Horndeski theories
  10. Introduction with a simple example in $D=4$ dimensions
  11. Covariant Galileons in $D$ dimensions
  12. Covariantized generalized Galileon and Horndeski theories
  13. Galileons and generalized galileons from branes
  14. Covariant multi field theories
  15. Conclusions