An Introduction to Chameleon Gravity

TL;DR

This paper introduces the chameleon scalar field, which varies its mass with local matter density, potentially mediating a detectable fifth force in space while remaining hidden in laboratory conditions.

Contribution

It provides a pedagogical overview of chameleon field theory, deriving equations of motion, discussing cosmological implications, and exploring simple solutions for experimental detection.

Findings

Chameleon field's mass increases with local matter density.

The fifth force mediated by the chameleon is suppressed in dense environments.

Potential detectability of the chameleon in space-based experiments.

Abstract

Following work by Khoury and Weltman, we introduce a scalar field phi, the chameleon, which is conformally coupled to matter. That is, matter experiences a metric which is a conformal transform (parametrized by phi) of the Einstein metric. The effective potential of the field phi is a sum of its self-interaction term and an exponential term due to the conformal coupling. Under certain conditions on the self-interaction and the coupling, this effective potential has a minimum which depends on the local matter density, as does its second derivative at the minimum. As a result, the scalar field acquires a mass which increases with local matter density. The field phi mediates a fifth force which is suppressed in the laboratory and in interactions between large bodies like planets, but which may be detectable between small test masses in space. In this pedagogical essay, we derive the equation of motion of phi, discuss chameleon-field cosmology, and examine some simple solutions with a view to experimental detection of the chameleon.