Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field

The existence of a primordial magnetic field at the last scattering surfacemay induce a measurable Faraday rotation in the polarization of the cosmicmicrowave background. We calculate the magnitude of this effect by evolving theradiative transfer equations for the microwave background polarization throughthe epoch of last scatter, in the presence of a magnetic field. For aprimordial field amplitude corresponding to a present value of $10^{-9}{\rm G}$(which would account for the observed galactic field if it were frozen in thepre-galactic plasma), we find a rotation angle of around $1^\circ$ at afrequency of 30 GHz. The statistical detection of this signal is feasible withfuture maps of the microwave background.Comment: 14 pages AASTeX with 2 embedded postscript figures, 44 k