Abstract
Generation of cosmic microwave background (CMB) elliptic polarization due to the Cotton–Mouton (CM) effect in a cosmic magnetic field is studied. We concentrate on the generation of CMB circular polarization and on the rotation angle of the CMB polarization plane from the decoupling time until at present. For the first time, a rather detailed analysis of the CM effect for an arbitrary direction of the cosmic magnetic field with respect to photon direction of propagation is done. Considering the CMB linearly polarized at the decoupling time, it is shown that the CM effect is one of the most substantial effects in generating circular polarization especially in the low part of the CMB spectrum. It is shown that in the frequency range 10^8 Hz le nu _0le 10^9 Hz, the degree of circular polarization of the CMB at present for perpendicular propagation with respect to the cosmic magnetic field is in the range 10^{-13}lesssim P_C(t_0)lesssim 7.65times 10^{-7} or Stokes circular polarization parameter 2.7 times 10^{-13} K lesssim |V(t_0)|lesssim 2 times 10^{-6} K for values of the cosmic magnetic field amplitude at present in the range 10^{-9} G lesssim Blesssim 8times 10^{-8} G. On the other hand, for not perpendicular propagation with respect to the cosmic magnetic field we find 10^{-15}lesssim P_C(t_0)lesssim 6times 10^{-12} or 2.72 times 10^{-15} K lesssim |V(t_0)| lesssim 10^{-11} K, for the same values of the cosmic magnetic field amplitude and same frequency range. Estimates on the rotation angle of the CMB polarization plane delta psi _0 due to the CM effect and constraints on the cosmic magnetic field amplitude from current constraints on delta psi _0 due to a combination of the CM and Faraday effects are found.
Highlights
In the recent years there have been several other theoretical studies exploring the possibility of cosmic microwave background (CMB) circular polarization from standard and non-standard effects and new experiments such as MIPOL [9] and SPIDER [10] aiming to detect it
In order to calculate the degree of circular polarization, let us use the results obtained in Sect. 4.3 that we found without any restriction on the magnitude of MF(T0)
In the previous section we studied the generation of the CMB circular polarization by calculating explicitly PC (T0) in various regimes
Summary
In the recent years there have been several other theoretical studies exploring the possibility of CMB circular polarization from standard and non-standard effects and new experiments such as MIPOL [9] and SPIDER [10] aiming to detect it. [19,20], I studied the most important magnetooptic effects which can generate CMB circular polarization when the CMB interacts with large-scale cosmic magnetic fields. There are some effects such as the photon-photon scattering in a cosmic magnetic field [19] and the free photonphoton scattering [13,17] which are linearly proportional to the CMB frequency and one might hope that the higher is the frequency, the stronger is the circular polarization signal. The CM effect is proportional to the square of the magnetic field amplitude, B2, and inversely proportional to the third power of the CMB frequency, namely ν−3 in the case of perpendicular propagation with respect to the cosmic magnetic field It is especially the scaling law with the frequency of ν−3 which makes the CM effect the most important effect in generating CMB circular polarization at low frequencies.
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