The new aspect of this approach is the isolation
of the *total* angular dependence of the modes by combining
the intrinsic angular structure with that of the plane-wave
spatial dependence. This property implies that the normal
modes correspond directly to angular structures on the sky
as opposed to the commonly employed technique that isolates
portions of
the *intrinsic* angular dependence and hence a
linear combination of observable modes [10].
Elements of this approach
can be found in earlier works (e.g. [6,7,11] for
the temperature and [3] for the scalar and
tensor polarization). We provide here a systematic study of
this technique which also provides for a substantial simplification of
the evolution equations and their integral solution
in §IIIC, including
the terms involving the radiation transport
of the CMB. We discuss in detail how the monopole, dipole
and quadrupole sources that enter into the radiation transport
problem project as anisotropies on the sky today.

Readers not interested in the formal details may skip this section on first reading and simply note that the temperature and polarization distribution is decomposed into the modes and with for scalar, vector and tensor metric perturbations respectively. In this representation, the geometric distinction between scalar, vector and tensor contributions to the anisotropies is clear as is the reason why they do not mix. Here the are the spin-2 spherical harmonics [12] and were introduced to the study of CMB polarization by [3]. The radial decompositions of the modes and (for ) isolate the total angular dependence by combining the intrinsic and plane wave angular momenta.