Polarization signal of distant clusters and reconstruction of primordial potential fluctuations - art. no. 123004

We examine the polarization signal of the cosmic microwave background radia tion associated with distant clusters. The polarization is induced by the T homson scattering of microwave photons with ionized gas of clusters and con tains information of quadrupole temperature anisotropies observed at the cl usters. The three-dimensional map of the signal is expressed in terms of th e spin-weighted harmonics for its angular dependence. Its radial dependence is expanded perturbatively with respect to the distances (equivalently red shifts) to the clusters. The independent information that we can extract fr om the map is clarified explicitly.