Introducing the Slotheon: a slow Galileon scalar field in curved space-time

TL;DR

This paper introduces the Slotheon, a scalar field in curved spacetime with a modified propagator that moves slower than usual due to a non-minimal coupling, and explores its properties and limitations.

Contribution

It defines covariant Galilean transformations in curved spacetime and constructs the Slotheon, a novel scalar field theory with unique slow-moving dynamics and specific black hole hair restrictions.

Findings

Slotheon moves slower than canonical scalar fields in gravity

Black holes cannot have Slotheonic hairs

The theory exhibits an asymptotic shift symmetry in certain regimes

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.