  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.
