A large scale coherent magnetic field : interactions with the free streaming particles and limits

In this paper, we have studied a magnetic field coherent over very large scales so that it can be considered homogeneous. We have shown that in the radiation dominaited era the well know Bianchi I solution for this geometry is isotrpized if a free straming relativistic  component is present and contributes sufficiently to the energy density. This mechanism is cis provided by the anisotropic presssure developped by the free streaming particles which counteracts the one from the magnetic field. This has been studied both numerically and analytically.