  We introduce a new formalism to describe the polarization signal of galaxy
clusters on the whole sky. We show that a sparsely sampled, half-sky map of the
cluster polarization signal at $z\sim 1$ would allow to better characterize the
very large scale density fluctuations. While the horizon length is smaller in
the past, two other competing effects significantly remove the contribution of
the small scale fluctuations from the quadrupole polarization pattern at $z\sim
1$. For the standard Lambda-CDM universe with vanishing tensor mode, the
quadrupole moment of the temperature anisotropy probed by WMAP is expected to
have a ~32% contribution from fluctuations on scales below 6.3h^{-1}Gpc. This
percentage would be reduced to ~2% level for the quadrupole moment of
polarization pattern at $z\sim 1$. A cluster polarization map at $z \sim 1$
would shed light on the potentially anomalous features of the largest scale
structure in the observable universe.
