Chameleon Gravity, Electrostatics, and Kinematics in the Outer Galaxy

TL;DR

This paper explores the chameleon mechanism in scalar fields, drawing analogies with electrostatics to calculate gravitational effects and violations of the equivalence principle in galactic outskirts.

Contribution

It introduces an electrostatic analogy for thin-shell conditions and applies the method of images to compute self-force effects in galactic environments.

Findings

Intermediate mass satellites can be up to 10% slower near thin shells.

The electrostatic analogy simplifies calculations of chameleon field effects.

Violation of equivalence principle varies with satellite mass and position.

Abstract

Light scalar fields are expected to arise in theories of high energy physics (such as string theory), and find phenomenological motivations in dark energy, dark matter, or neutrino physics. However, the coupling of light scalar fields to ordinary (or dark) matter is strongly constrained from laboratory, solar system, and astrophysical tests of fifth force. One way to evade these constraints in dense environments is through the chameleon mechanism, where the field's mass steeply increases with ambient density. Consequently, the chameleonic force is only sourced by a thin shell near the surface of dense objects, which significantly reduces its magnitude. In this paper, we argue that thin-shell conditions are equivalent to "conducting" boundary conditions in electrostatics. As an application, we use the analogue of the method of images to calculate the back-reaction (or self-force) of an object around a spherical gravitational source. Using this method, we can explicitly compute the violation of equivalence principle in the outskirts of galactic haloes (assuming an NFW dark matter profile): Intermediate mass satellites can be slower than their larger/smaller counterparts by as much as 10% close to a thin shell.