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We present a novel mathematical formalism that allows to easily compute theexpected kinetic Sunyaev Zeldovich (kSZ) signal in intensity and polarizationdue to an anisotropic primordial Cosmic Microwave Background (CMB). We derivethe expected intensity and polarization distortions in the direction ofnon-moving galaxy clusters and then we generalize our calculations for non-zeropeculiar velocity. We show that, in the direction of moving clusters, low CMBmultipoles impose intensity and polarization spectral distortions withdifferent frequency dependences. The polarization signal primarily probes thequadrupole moment of the CMB, with a significant contribution from theprimordial dipole and octupole moments. For a typical cluster velocity of 1000km/s, corrections to the quadrupole-induced polarization of a non-movingcluster are of the order of 2-10% between 200-600 GHz, and depend on cluster'sposition on the sky, velocity magnitude and direction of motion. We also findthat the angular dependence of the signal varies with frequency of observation.The distinct frequency and angular dependences of the polarization induced bythe primordial dipole and octupole can be exploited to measure them despiteother physical effects and foregrounds. Contrary to polarization, intensitydistortions are affected by all the CMB multipoles, so they cannot be readilyused to probe the low multipoles at higher redshifts. However, correlationsbetween intensity and polarization signals, can be used to enhance the signalto noise ratio for the measurements of the primordial dipole, quadrupole andoctupole. The more general calculation of the aberration kernel presented inthis work has applications reaching beyond the SZ cluster science addressedhere. For example, it can be exploited to the deboost/deaberrate CMB multipolesas observed in our local frame.

physical review. d/physical review. d.

Kinetic Sunyaev Zeldovich effect in an anisotropic CMB model: measuring  low multipoles of the CMB at higher redshifts using intensity and  polarization spectral distortions