Faraday rotation, stochastic magnetic fields and CMB maps

TL;DR

This paper develops a comprehensive theoretical framework to analyze the effects of primordial magnetic fields on CMB polarization, specifically Faraday rotation, within the magnetized ΛCDM model, leading to the first magnetized CMB maps.

Contribution

It introduces an advanced physical and numerical framework for calculating CMB polarization in magnetized plasmas, including the first magnetized CMB temperature and polarization maps within the minimal ΛCDM model.

Findings

First complete calculation of Faraday-induced B-mode polarization.

Generation of the first magnetized CMB temperature and polarization maps.

Framework enables direct comparison with Planck satellite data.

Abstract

The high- and 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 $\Lambda$CDM paradigm (m$\Lambda$CDM). 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 m$\Lambda$CDM 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.