Faraday Rotation of the Cosmic Microwave Background Polarization and Primordial Magnetic Field Properties

Measurements of the Faraday rotation of the cosmic microwave background radiation (CMBR) polarization could provide evidence for the existence of primordial magnetic fields. The Faraday rotation could also allow the study of some properties of these fields. In this paper, we calculate the angular dependence of the Faraday rotation correlator for different assumptions about the spectral index and correlation length of the magnetic field. We show that the helical part of the magnetic field does not make any contribution to the correlator. We stress the importance of the angular resolution of the detector in the Faraday rotation measure, showing that it could severely reduce the effect, even for a relatively large magnetic field correlation length.