Comments on Galileons

TL;DR

This paper explores the relationship between Galileons and Universal Field Equations, showing that Galileons are Kaluza-Klein reductions of these equations, and presents solutions and multi-field extensions.

Contribution

It reveals that Galileons are Kaluza-Klein reductions of Universal Field Equations and develops multi-field extensions from a fluid dynamics formalism.

Findings

Galileons are related to Universal Field Equations.

An implicit solution to the equations of motion is provided.

Multi-field extensions are derived from fluid dynamics formalism.

Abstract

The recent progress in the study of Galileons, i.e. equations of second order with an action invariant under a Galilean transformation is related to work on `Universal Field Equations' \cite{dbfgov} which are second order equations arising by an iterative procedure from arbitrary Lagrangians of weight one in their first derivatives. It is pointed out that the Galileon is simply a Kaluza-Klein reduction of a Universal Field Equation. An implicit solution to the equation of motion is presented, and a class of explicit solutions pointed out. The multi-field extensions of both types of equations are derived from a first order formalism, which is simply the substantive derivative of fluid dynamics.