CMB anisotropies: Total angular momentum method

A total angular momentum representation simplifies the radiation transport problem for temperature and polarization anisotropy in the cosmic microwave background (CMB). Scattering terms couple only the quadrupole moments of the distributions and each moment corresponds directly to the observable angular pattern on the sky. We develop and employ these techniques to study the general properties of anisotropy generation from scalar, vector, and tensor perturbations to the metric and the matter, both in the cosmological fluids and from any seed perturbations (e.g., defects) that may be present. The simpler, more transparent form and derivation of the Boltzmann equations brings out the geometric and model-independent aspects of temperature and polarization anisotropy formation. Large angle scalar polarization provides a robust means to distinguish between isocurvature and adiabatic models for structure formation in principle. Vector modes have the unique property that the CMB polarization is dominated by magnetic-type parity at small angles (a factor of $6$ in power compared with $0$ for the scalars and $8/13$ for the tensors) and hence potentially distinguishable independent of the model for the seed. The tensor modes produce a different sign from the scalars and vectors for the temperature-polarization correlations at large angles. We explore conditions under which one perturbation type may dominate over the others including a detailed treatment of the photon-baryon fluid before recombination.