Faraday Rotation of Microwave Background Polarization by a Primordial Magnetic Field

The existence of a primordial magnetic field at the last scattering surface may induce a measurable Faraday rotation in the polarization of the cosmic microwave background. We calculate the magnitude of this effect by evolving the radiative transfer equations for the microwave background polarization through the epoch of last scatter, in the presence of a magnetic field. For a primordial field amplitude corresponding to a present value of ${10}^{-9}\mathrm{G}$ (which would account for the observed galactic field if it were frozen in the pre-galactic plasma), we find a rotation angle of around $1^{\circ }$ at a frequency of 30 GHz. The statistical detection of this signal is feasible with future maps of the microwave background.