Circular dichroism, magnetic knots, and the spectropolarimetry of the cosmic microwave background

Abstract

When the last electron-photon scattering takes place in a magnetized environment, the degree of circular polarization of the outgoing radiation depends upon the magnetic field strength. After deriving the scattering matrix of the process, the generalized radiative transfer equations are deduced in the presence of the relativistic fluctuations of the geometry and for all the four brightness perturbations. The new system of equations is solved under the assumption that the incident radiation is not polarized. The induced $V$-mode polarization is analyzed both analytically and numerically. The corresponding angular power spectra are calculated and compared with the measured (or purported) values of the linear polarizations (i.e. $E$ mode and $B$ mode) as they arise in the concordance model and in its neighboring extensions. Possible connections between the $V$-mode polarization of the cosmic microwave background and the topological properties of the magnetic flux lines prior to equality are outlined and briefly explored in analogy with the physics of magnetized sunspots.