Higher derivative SVT theories from Kaluza-Klein reductions of Horndeski theory

TL;DR

This paper derives higher derivative vector-tensor theories from Kaluza-Klein reductions of 5D Horndeski, resulting in 4D models that maintain gauge invariance and avoid Ostrogradsky ghosts, expanding the framework for dark energy interactions.

Contribution

It provides a detailed derivation of 4D higher derivative SVT theories from 5D Horndeski via Kaluza-Klein reduction, including scalar and vector sectors with gauge invariance.

Findings

Derived all U(1) gauge invariant vector Galileons in 4D from 5D Horndeski

Constructed consistent higher derivative vector-scalar couplings without ghosts

Extended Horndeski theory to include G_5(π,X) and G_6(π,X) potentials

Abstract

It was recently pointed out that some precise Photon-Galileon couplings in four dimensions (4D) -- inspired by a higher dimensional reduction -- are enough to obtain a Horndeski theory that is less constrained by the stringent experimental bounds on the speed of Gravitational Waves. They imply the constancy of the ratio of speed of gravity to light throughout cosmic evolution. This holds even if we include the general scalar potentials $G_4 (\pi,X)$ and $G_5 (\pi)$. In this paper we go into the details of this 4D Luminal extension of Horndeski theory including its scalar sector. We also present the complete action including the general $G_5(\pi,X),\, G_6(\pi,X)$ scalar potentials. Thus we show all the $U(1)$ gauge invariant vector Galileons in 4D that result from a Kaluza-Klein dimensional reduction from 5D Horndeski. They provide a {\it consistent} coupling of a higher derivative vector to scalar modifications of gravity -- namely, without inducing Ostrogradsky ghosts and keeping gauge invariance -- in the aim to explore more universal couplings of dark energy to other matter, such as vectors and in particular the Photon.