waynehu
Professor,
Department of Astronomy and Astrophysics
University of Chicago
The considerations of §2 imply that scalars, vectors,
and tensors generate distinct patterns in the polarization of the CMB.
However, although they separate cleanly into 
polarization
patterns for a single plane wave perturbation in the coordinate
system referenced to 
, in general there will exist a spectrum of
fluctuations each with a different .
Therefore the polarization pattern on the sky does not separate into
modes. In fact, assuming statistical isotropy, one expects
the ensemble averaged power for each multipole 
to be independent of m.
Nonetheless, certain properties of the polarization patterns discussed in the
last section do survive superposition of the perturbations: in particular,
its parity and its correlation with the temperature fluctuations.
We now discuss how one can describe polarization patterns on the sky arising
from a spectrum of modes.
Next: Electric and Magnetic Modes