Optical activity of a neutrino gas

For photons that propagate through a gas of neutrinos with a non-zero chemical potential, the left-handed and right-handed polarization modes acquire different dispersion relations. This is due to the CP and CPT odd terms induced by such a background on the photon self-energy. We present a detailed calculation of this effect, which does not depend on any physical assumptions beyond those of the standard electroweak model. Some possible cosmological and astrophysical implications of our results are considered in several contexts, including the recent discussions regarding the rotation of the plane of polarization of electromagnetic waves over cosmological distances.