Power Spectra of CMB Polarization by Scattering in Clusters

Mapping CMB polarization is an essential ingredient of current cosmological research. Particularly challenging is the measurement of an extremely weak B-mode polarization that can potentially yield unique insight on inflation. Achieving this objective requires very precise measurements of the secondary polarization components on both large and small angular scales. Scattering of the CMB in galaxy clusters induces several polarization effects whose measurements can probe cluster properties. Perhaps more important are levels of the statistical polarization signals from the population of clusters. Power spectra of five of these polarization components are calculated and compared with the primary polarization spectra. These spectra peak at multipoles $\ell \geq 3000$, and attain levels that are unlikely to appreciably contaminate the primordial polarization signals.