Faraday rotation, stochastic magnetic fields and CMB maps

The highand low-frequency descriptions of the pre-decoupling plasma are deduced from the Vlasov-Landau treatment generalized to curved space-times and in the presence of the relativistic fluctuations of the geometry. It is demonstrated that the interplay between one-fluid and two-fluid treatments is mandatory for a complete and reliable calculation of the polarization observables. The Einstein-Boltzmann hierarchy is generalized to handle the dispersive propagation of the electromagnetic disturbances in the pre-decoupling plasma. Given the improved physical and numerical framework, the polarization observables are computed within the magnetized ΛCDM paradigm (mΛCDM). In particular, the Faraday-induced B-mode is consistently estimated by taking into account the effects of the magnetic fields on the initial conditions of the Boltzmann hierarchy, on the dynamical equations and on the dispersion relations. The complete calculations of the angular power spectra constitutes the first step for the derivation of magnetized maps of the CMB temperature and polarization which are here obtained for the first time and within the minimal mΛCDM model. The obtained results set the ground for direct experimental scrutiny of large-scale magnetism via the low and high frequency instruments of the Planck explorer satellite. Electronic address: [email protected] Electronic address: [email protected] 1 Plasma hierarchies and plasma descriptions Prior to matter-radiation equality and throughout decoupling the number of charge carriers present within the Debye sphere is, overall, inversely proportional to the baryonic concentration. The corresponding (dimensionless) plasma parameter [1, 2, 3] is O(10−7) and, more specifically gplasma = 1 VDn0xe = 24e √ ζ(3) π √ xeηb0 = 2.308× 10 √ xe ( h0Ωb0 0.02273 )1/2 , VD = 4 3 πλD, λD = √