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Polarization Patterns


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 tex2html_wrap_inline1044 polarization patterns for a single plane wave perturbation in the coordinate system referenced to tex2html_wrap_inline1162 , in general there will exist a spectrum of fluctuations each with a different tex2html_wrap_inline1162 . Therefore the polarization pattern on the sky does not separate into tex2html_wrap_inline1044 modes. In fact, assuming statistical isotropy, one expects the ensemble averaged power for each multipole tex2html_wrap_inline1272 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 tex2html_wrap_inline1162 modes.