No-Go Theorems for Generalized Chameleon Field Theories

TL;DR

This paper proves two theorems that limit the cosmological influence of chameleon-like scalar fields, showing they cannot cause self-acceleration or significantly affect linear-scale growth, thus acting more like dark energy.

Contribution

It provides general no-go theorems that restrict the impact of chameleon, symmetron, and dilaton scalar fields on cosmology, especially on linear growth and acceleration.

Findings

Scalar field's Compton wavelength is at most Mpc scale today.

Conformal factor remains nearly constant over the last Hubble time.

Chameleon fields cannot produce self-acceleration in cosmology.

Abstract

The chameleon, or generalizations thereof, is a light scalar that couple to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: i) the Compton wavelength of such a scalar can be at most Mpc at present cosmic density, which restricts its impact to non-linear scales; ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time, which precludes the possibility of self-acceleration. These results imply that chameleon-like scalar fields have a negligible effect on the linear-scale growth history; theories that invoke a chameleon-like scalar to explain cosmic acceleration rely on a form of dark energy rather than a genuine modified gravity effect. Our analysis applies to a broad class of chameleon, symmetron and dilaton theories.