Large scale anisotropies and polarization of the microwave background radiation in homogeneous cosmologies

The polarization and anisotropy of the cosmological microwave background radiation on large angular scales are discussed. A quadrupole anisotropy in the expansion of the universe (shear) is considered in realistic cosmological models and the resulting anisotropies and polarization of the radiation are calculated. The role of spatial curvature is considered separately, and it is found to have two profound effects: first, in closed models only, the direction of polarization of the radiation will appear at observation to be twisted relative to the anisotropy; the existence of this twist implies that the closed universe has a handedness property. Second, in open models a quadrupole anisotropy may be distorted by the spatial curvature so that it resembles a dipole; in the extreme case all the aniso­tropy is confined to a region of small angular diameter (a ‘spot’). Following previous work by Dautcourt and Rose, a transfer equation for polarized radiation in a general curved space-time is derived. The effect of Thomson scattering by free electrons is included, and the equation is separated into those for the multipoles up to quadrupole by expanding in polynomials formed from spin-weighted spherical harmonics. A numerical integration of the equations is described, and the results are presented for the twist angle, the dipole and quadrupole anisotropies, the degree of polarization in the quadrupole mode and the ratio of polarization to quadrupole aniso­tropy in all models considered. The twist of polarization in closed models is large and should be easily observable if the polarization could be. This result suggests an important observational test of the spatial curvature of the standard models. The dipole produced in open models, due to distortion by the spatial curvature, is prominent; it appears unlikely that an intrinsic dipole to quadrupole ratio of less than unity arises in any open models in which the effect occurs when the density is below one-half the critical density. Finally, the ratio of polarization to anisotropy is expected to be a good indicator of the presence of shear, and is sensitive to the ionization history of the matter.