A slow Galileon scalar field in curved space-time

In this paper, we define covariant Galilean transformations in curved space-time 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 setup. This property is achieved by a nonminimal 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 noncanonical coupling dominates over the canonical one.