Milli-charged fermion vacuum polarization in cosmic magnetic fields and
  generation of CMB elliptic polarization
  The contribution of one loop milli-charged fermion vacuum polarization in
cosmic magnetic field to the cosmic microwave background (CMB) polarization is
considered. Exact and perturbative solution of the density matrix equations of
motion in terms of the Stokes parameters are presented. For linearly polarized
CMB at decoupling time, it is shown that propagation of CMB photons in cosmic
magnetic field would generate elliptic polarization (circular and linear) of
the CMB due to milli-charged fermion vacuum polarization. Analytic expressions
for the degree of circular polarization and rotation angle of polarization
plane of the CMB are presented. Depending on the ratio of milli-charged fermion
relative charge to mass, $\epsilon/m_\epsilon$, and CMB observation frequency,
it is shown that the acquired CMB degree of circular polarization could be of
the order of magnitude $P_C(T_0)\sim 10^{-10}- 10^{-6}$ in the best scenario.
The effect studied 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.
