Abstract
(abridged) A detailed examination of the evolution of stochastic magnetic fields between high cosmic temperatures and the present epoch is presented. A simple analytical model matching the results of the 3D MHD simulations allows for the prediction of present day magnetic field correlation lengths and energy. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields. (b) There exists a correlation between the strength of the magnetic field, B, at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ~ 5x10^{-12} (L/kpc) Gauss, where L is the correlation length determined by the initial magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B~10^{-9} Gauss on ~ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l~10^6 where the signal is predicted to be the strongest. (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10^{-12} - 10^{-11} Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.