Evolution of cosmic magnetic fields: From the very early Universe, to recombination, to the present

A detailed numerical and analytical examination of the evolution of stochastic magnetic fields between a putative magnetogenesis era at high cosmic temperatures Tsimilar to100 MeV-100 GeV and the present epoch is presented. The analysis includes all relevant dissipation processes, such as neutrino- and photon-induced fluid viscosities as well as ambipolar and hydrogen diffusion. A simple and intuitive analytical model matching the results of the three-dimensional MHD simulations allows for the prediction of prerecombination and present day magnetic field correlation lengths and energy densities as a function of initial magnetic field energy density, helicity, and spectral index. Our conclusions are multifold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields at the present. Furthermore, the simulations show a self-similarity in the evolution of maximally helical fields implying a seemingly acausual amplification of magnetic fields on large scales is observed. (b) There exists a correlation between the strength of the magnetic field B at the peak of its spectrum and the location of the peak, given at the present epoch by Bapproximate to5x10(-12) G(L/kpc), where L is the magnetic field correlation length determined by the initial properties of the magnetic field. (c) Concerning studies of the generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of Bsimilar to10(-9) G on greater than or similar to10 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 lsimilar to10(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 (precollapse) strength 10(-12)-10(-11) G with correlation lengths in the kpc range and would also exist in voids of galaxies.