The Chameleon Effect in the Jordan Frame of the Brans--Dicke Theory

TL;DR

This paper explores the chameleon effect in different conformal frames of the Brans--Dicke theory, highlighting the challenges in reconciling local and cosmological bounds and showing conditions under which it reduces to general relativity with a cosmological constant.

Contribution

It provides a detailed analysis of the chameleon effect in Jordan and string frames of Brans--Dicke theory, extending the understanding beyond the Einstein frame and examining cosmological implications.

Findings

Local and cosmological bounds are difficult to reconcile with a single chameleon potential.

Brans--Dicke theory can effectively become general relativity with a cosmological constant in regions with constant matter density.

De Sitter--general relativity is a global attractor only for quadratic or asymptotically quadratic potentials.

Abstract

In this paper we investigate the chameleon effect in the different conformal frames of the Brans--Dicke theory. Given that, in the standard literature on the subject, the chameleon is described in the Einstein frame almost exclusively, here we pay special attention to the description of this effect in the Jordan and in the string frames. It is shown that, in general, terrestrial and solar system bounds on the mass of the BD scalar field, and bounds of cosmological origin, are difficult to reconcile at once through a single chameleon potential. We point out that, in a cosmological context, provided that the effective chameleon potential has a minimum within a region of constant density of matter, the Brans--Dicke theory transmutes into general relativity with a cosmological constant, in that region. This result, however, can be only locally valid. In cosmological settings de Sitter--general relativity is a global attractor of the Brans--Dicke theory only for the quadratic potential $V(\phi)=M^2\phi^2$, or for potentials that asymptote to $M^2\phi^2$.