Millicharged fermion vacuum polarization in a cosmic magnetic field and generation of CMB elliptic polarization

The contribution of one-loop millicharged fermion vacuum polarization in a cosmic magnetic field to the cosmic microwave background (CMB) polarization is considered. Exact and perturbative solutions of the density matrix equations of motion in terms of the Stokes parameters are presented. For linearly polarized CMB at the decoupling time, it is shown that the propagation of CMB photons in a cosmic magnetic field would generate elliptic polarization (circular and linear) of the CMB due to millicharged fermion vacuum polarization. Analytic expressions for the degree of circular polarization and rotation angle of the polarization plane of the CMB are presented. Depending on the ratio of millicharged fermion relative charge to mass, epsilon/m(epsilon), magnetic field amplitude, and CMB observation frequency, it is shown that the acquired CMB degree of circular polarization could be of the order of magnitude PC(T-0) similar to 10(-10)- 10(-6) in the best scenario for a canonical value of magnetic field amplitude of the order of similar to nG and epsilon/m(epsilon) similar to 10(-4)- few x 10(-3). The mechanism considered in this work generates CMB polarization even in the case when the CMB is initially in thermal equilibrium. Limits on the magnetic field amplitude due to prior-decoupling CMB polarization are presented.