Magnetic field contribution to the last electron-photon scattering

TL;DR

This paper investigates how magnetic fields influence electron-photon scattering in the early universe, affecting the polarization and anisotropies of the cosmic microwave background across different modes and magnetic field configurations.

Contribution

It introduces a comprehensive analysis of magnetic field effects on scattering, including arbitrary magnetic field directions and all geometric modes, which was not previously addressed.

Findings

Magnetic fields contribute to the Stokes matrix and transport equations.

The impact of magnetic fields on relic vector and tensor modes is characterized.

Averaging over magnetic field orientations is explicitly performed.

Abstract

When the cosmic microwave photons scatter electrons just prior to the decoupling of matter and radiation, magnetic fields do contribute to the Stokes matrix as well as to the scalar, vector and tensor components of the transport equations for the brightness perturbations. The magnetized electron-photon scattering is hereby discussed in general terms by including, for the first time, the contribution of magnetic fields with arbitrary direction and in the presence of the scalar, vector and tensor modes of the geometry. The propagation of relic vectors and relic gravitons is discussed for a varying magnetic field orientation and for different photon directions. The source terms of the transport equations in the presence of the relativistic fluctuations of the geometry are also explicitly averaged over the magnetic field orientations and the problem of a consistent account of the small-scale and large-scale magnetic field is briefly outlined.