Perturbation Evolution

  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 radiation transport of the CMB under Thomson scattering, including polarization (§IIIB), than that obtained first by [16]. The complete evolution equations, given in §IIIC, are again substantially simpler in form than those of prior works where they overlap [3,4,10,11] 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.