Magneto-optic effects of the cosmic microwave background

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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.