Magneto-optic effects of the Cosmic Microwave Background
  Generation of magneto-optic effects by the interaction of the CMB with cosmic
magnetic fields is studied. Effects which generate polarization such as the
Cotton-Mouton effect, vacuum polarization and photon-pseudoscalar mixing in
external magnetic field are studied. Considering the CMB linearly polarized at
decoupling time, it is shown that photon-pseudoscalar mixing in external
magnetic field, the Cotton-Mouton effect in plasma and the vacuum polarization
in cosmic magnetic field, would generate elliptic polarization of the CMB
depending on the photon frequency and magnetic field strength. Among standard
magneto-optic effects, the Cotton-Mouton effect in plasma turns out to be the
dominant effect in the generation of CMB elliptic polarization in the low
frequency part $\nu_0 \sim 10^8-10^9$ Hz with degree of circular polarization
$P_C(T_0)\simeq 10^{-10}-10^{-6}$ for magnetic field amplitude $B_{e0}\sim
100\, \text{nG}-1$ nG. The vacuum polarization in magnetic field is the
dominant process in the high frequency part $\nu_0\geq 10^{10}$ Hz where the
degree of circular polarization at present is $P_C(T_0)\lesssim 10^{-11}$ in
the best scenario. It is shown that photon-pseudoscalar particle mixing in
cosmic magnetic field generates elliptic polarization of the CMB as well and
even in the case of initially unpolarized CMB. New limits/constraints on the
pseudoscalar parameter space are found. By using current limit on the degree of
circular polarization of the CMB, the upper limit of
$|g_{\phi\gamma}|<4.29\times 10^{-19}(\text{G}/B_{e0})$ GeV$^{-1}$ for
$m_\phi<1.6\times 10^{-14}$ eV in the weak mixing case is found. If
$|g_{\phi\gamma}| < 1.17\times 10^{-24}(\text{G}/B_{e0})$ GeV$^{-1}$, a value
of the order $|g_{\phi\gamma}|\simeq 10^{-26}(\text{G}/B_{e0})$ GeV$^{-1}$ for
$m_\phi\simeq 1.6\times 10^{-14}$ eV in the resonant case, from large scale
temperature anisotropy is obtained.
