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.
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