Kinetic Sunyaev Zeldovich effect in an anisotropic CMB model: measuring
  low multipoles of the CMB at higher redshifts using intensity and
  polarization spectral distortions
  We present a novel mathematical formalism that allows to easily compute the
expected kinetic Sunyaev Zeldovich (kSZ) signal in intensity and polarization
due to an anisotropic primordial Cosmic Microwave Background (CMB). We derive
the expected intensity and polarization distortions in the direction of
non-moving galaxy clusters and then we generalize our calculations for non-zero
peculiar velocity. We show that, in the direction of moving clusters, low CMB
multipoles impose intensity and polarization spectral distortions with
different frequency dependences. The polarization signal primarily probes the
quadrupole moment of the CMB, with a significant contribution from the
primordial dipole and octupole moments. For a typical cluster velocity of 1000
km/s, corrections to the quadrupole-induced polarization of a non-moving
cluster are of the order of 2-10% between 200-600 GHz, and depend on cluster's
position on the sky, velocity magnitude and direction of motion. We also find
that the angular dependence of the signal varies with frequency of observation.
The distinct frequency and angular dependences of the polarization induced by
the primordial dipole and octupole can be exploited to measure them despite
other physical effects and foregrounds. Contrary to polarization, intensity
distortions are affected by all the CMB multipoles, so they cannot be readily
used to probe the low multipoles at higher redshifts. However, correlations
between intensity and polarization signals, can be used to enhance the signal
to noise ratio for the measurements of the primordial dipole, quadrupole and
octupole. The more general calculation of the aberration kernel presented in
this work has applications reaching beyond the SZ cluster science addressed
here. For example, it can be exploited to the deboost/deaberrate CMB multipoles
as observed in our local frame.
