Introducing the Slotheon: a slow Galileon scalar field in curved space-time
Cristiano Germani, Luca Martucci, Parvin Moyassari
TL;DR
This work formulates covariant Galilean (Galileon) transformations in curved spacetime and classifies scalar Lagrangians preserving the symmetry, identifying the Slotheon as a Galilean-invariant field with a non-minimal derivative coupling to the Einstein tensor $G^{\mu\nu}$ that slows its dynamics when gravity is active. It shows that gauging the shift symmetry in the high-friction, small-derivative regime yields an approximate symmetry that mixes $\pi$ with the metric, enabling a robust EFT with a Planck-scale cutoff and an Einstein-frame description. A central result is a no-hair theorem for Slotheonic black holes, proving that spherically symmetric solutions have no Slotheon hair and reduce to Schwarzschild, which supports the theory’s stability. The paper also uncovers an asymptotic local shift symmetry during inflation in the high-friction limit, underpinning UV-protected inflation (GEF/New Higgs inflation) and soft-breaking by the potential, with implications for quantum corrections and model-building in curved-space scalar theories.$
Abstract
In this paper we define covariant Galilean transformations in curved spacetime and find all scalar field theories invariant under this symmetry. The Slotheon is a Galilean invariant scalar field with a modified propagator such that, whenever gravity is turned on and energy conditions are not violated, it moves "slower" than in the canonical set-up. This property is achieved by a non-minimal derivative coupling of the Slotheon to the Einstein tensor. We prove that spherically symmetric black holes cannot have Slotheonic hairs. We then notice that in small derivative regimes the theory has an asymptotic local shift symmetry whenever the non-canonical coupling dominates over the canonical one.