Ghost-free, gauge invariant SVT generalizations of Horndeski theory

TL;DR

The work extends Horndeski gravity by embedding a U(1) gauge-invariant vector into a Scalar–Vector–Tensor framework, preserving second-order equations of motion and connecting to the Kaluza–Klein reduction of 5D Horndeski. It constructs a general SVT action from a 33-term vector basis with ghost-free restrictions, and shows how Horndeski remains the scalar–tensor core while the vector sector remains nontrivial. A subset, the luminal SVT generalizations, enforces equal propagation speeds for tensor and vector modes on any cosmological background, introducing an extra vector-sector freedom through a function $f(\pi, X)$ and linking to the KK–SVT and $G_4,G_5$ couplings; however, nonzero $G_{5X}$ is constrained. This framework maintains compatibility with gravitational-wave speed constraints and offers a pathway to independent vector modifications within a healthy, ghost-free theory, with potential applications to dark energy and multi-messenger tests.

Abstract

We analyze the generalizations of Kaluza--Klein compactifications of 5D Horndeski theory. They are Scalar--Vector--Tensor (SVT) theories with higher derivatives in the action, but with second order equations of motion. The vector field is invariant under a U(1) gauge transformation and the Scalar--Tensor sector corresponds to Horndeski theory. A subclass of these SVT theories is such that the Horndeski functions $G_4(π,X)$ and $G_5(π)$ remain free, while the speed of the tensor and vector modes is exactly the same. We show a subclass where the vector sector retains freedom through new functions of $π,\, X$ while the speed of the vector modes still tracks the speed of the tensor modes.