Reconstruction of CMB Temperature Anisotropies with Primordial CMB
  Induced Polarization in Galaxy Clusters
  Scattering of cosmic microwave background (CMB) radiation in galaxy clusters
induces polarization signals determined by the quadrupole anisotropy in the
photon distribution at the location of clusters. This "remote quadrupole"
derived from the measurements of the induced polarization in galaxy clusters
provides an opportunity of reconstruction of local CMB temperature
anisotropies. In this {\em Letter} we develop an algorithm of the
reconstruction through the estimation of the underlying primordial
gravitational potential, which is the origin of the CMB temperature and
polarization fluctuations and CMB induced polarization in galaxy clusters. We
found a nice reconstruction for the quadrupole and octopole components of the
CMB temperature anisotropies with the assistance of the CMB induced
polarization signals. The reconstruction can be an important consistency test
on the puzzles of CMB anomaly, especially for the low quadrupole and axis of
evil problems reported in WMAP and Planck data.
