Effect of a chameleon scalar field on the cosmic microwave background

Abstract

We show that a direct coupling between a chameleonlike 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 ${\mathcal{P}}_{\mathrm{Coma}}(204\text{ }\text{ }\mathrm{GHz})<6.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ at 95% confidence, corresponding to an upper bound on the coupling strength of ${g}_{\mathrm{eff}}^{(\mathrm{cell})}<2.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$ or ${g}_{\mathrm{eff}}^{(\mathrm{Kolmo})}<(7.2--32.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}1}$, 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 farther toward 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 chameleonlike scalar field. These predictions could be verified or constrained by future CMB experiments.