Up: CMB ANISOTROPIES: TOTAL ANGULAR
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We discuss here the evolution of perturbations in the normal
modes of §II. We first review the decomposition
of perturbations in the metric and stress-energy tensor into
scalar, vector and tensor types (§IIIA). We
further divide the stress-energy tensor into fluid contributions,
applicable to the usual particle species,
and seed perturbations, applicable to cosmological defect models.
We then employ the
techniques developed in §II
to obtain a new, simpler derivation and form of the
of the CMB under Thomson scattering, including polarization
than that obtained first by .
The complete evolution equations, given in
§IIIC, are again substantially simpler in form
than those of prior works where they overlap
and treats the case of vector perturbations. Finally
in §IIID, we derive the formal integral solutions
through the use of the radial functions of §IIB
and discuss their geometric interpretation. These solutions
encapsulate many of the important results.