The Effect of a Chameleon Scalar Field on the Cosmic Microwave
  Background
  We show that a direct coupling between a chameleon-like scalar field and
photons can give rise to a modified Sunyaev-Zel'dovich (SZ) effect in the
Cosmic Microwave Background (CMB). The coupling induces a mixing between
chameleon particles and the CMB photons when they pass through the magnetic
field of a galaxy cluster. Both the intensity and the polarization of the
radiation are modified. The degree of modification depends strongly on the
properties of the galaxy cluster such as magnetic field strength and electron
number density. Existing SZ measurements of the Coma cluster enable us to place
constraints on the photon-chameleon coupling. The constrained conversion
probability in the cluster is P_Coma(204 GHz) < 6.2 * 10^{-5} at 95%
confidence, corresponding to an upper bound on the coupling strength of g_eff <
2.2 * 10^{-8} GeV^-1 or g_eff < 7.2-32.5 * 10^{-10} GeV^-1, depending on the
model that is assumed for the cluster magnetic field structure. We predict the
radial profile of the chameleonic CMB intensity decrement. We find that the
chameleon effect extends further towards the edges of the cluster than the
thermal SZ effect. Thus we might see a discrepancy between the X-ray emission
data and the observed SZ intensity decrement. We further predict the expected
change to the CMB polarization arising from the existence of a chameleon-like
scalar field. These predictions could be verified or constrained by future CMB
experiments.
