Galileons from Lovelock actions

TL;DR

This work shows how covariant Galileon actions naturally emerge from standard Kaluza-Klein compactifications of higher-dimensional Lovelock gravity, with the dilaton $\pi$ acting as the Galileon. The authors derive a complete decomposition in arbitrary $D$, revealing that each compactification term preserves second-order equations for both $g_{\mu\nu}$ and $\pi$, and identify a precise relationship between the $\mathcal{K}^n$ and $\mathcal{L}^n$ structures up to total derivatives. They classify the independent Galilean terms, separating curvature-only Lovelock pieces from scalar-tensor couplings, and show that in $D=4$ the known covariant Galileons reappear alongside two additional second-order couplings, one of which is new. The results unify geometric origins of Galileons, clarify their structural completeness, and point to natural extensions to multi-field or vector Galileons with potential cosmological relevance, such as Galilean inflation.

Abstract

We demonstrate how, for an arbitrary number of dimensions, the Galileon actions and their covariant generalizations can be obtained through a standard Kaluza-Klein compactification of higher-dimensional Lovelock gravity. In this setup, the dilaton takes on the role of the Galileon. In addition, such compactifications uncover other more general Galilean actions, producing purely second-order equations in the weak-field limit, now both for the Galileon and the metric perturbations.