Polarization of the Microwave Background in Inflationary Cosmology

Abstract

We evaluate the large scale polarization of the cosmic microwave background induced, via Thomson scattering prior to decoupling, by nearly scale-invariant spectra of scalar and tensor metric perturbations, such as those predicted by most inflationary models of the early Universe. We solve the radiative transfer equation for the polarized photon distribution function analytically, for wavelengths of order or larger than the horizon size at decoupling, assuming no reionization. The induced polarization is proportional to the redshift induced by the perturbations at decoupling and to the duration of the decoupling transition. Normalizing the spectra to the quadrupole anisotropy measured by the COBE satellite, the expected degree of linear polarization is $P\lsim 10^{-7}$, more than two orders of magnitude smaller than current bounds. The dependence of $P$ with the tilt in the spectrum away from scale invariance is too weak to be of observational relevance or to provide a sensitive discrimination between scalar and tensor fluctuations. The variation of $P$ with the angular scale is significant.