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 scattering, in the presence of a magnetic field. For a primordial field amplitude corresponding to a present value of 10(-9) G (which would account for the observed galactic held if it were frozen in the pregalactic plasma), we find a rotation angle of similar to 1 degrees at a frequency of 30 GHz. The statistical detection of this signal will be feasible with future maps of the microwave background.