Abstract
We present results of a detailed and fully non-linear numerical and analytical investigation of magnetic field evolution from the very earliest cosmic epochs to the present. We find that, under reasonable assumptions concerning the efficiency of a putative magnetogenesis era during cosmic phase transitions, surprisingly strong magnetic fields 10^{-13} - 10^{-11} Gauss, on comparatively small scales 100 pc - 10 kpc may survive to the present. Building on prior work on the evolution of magnetic fields during the course of gravitational collapse of a cluster, which indicates that pre-collapse fields of 4\times 10^{-12} Gauss extant on small scales may suffice to produce clusters with acceptable Faraday rotation measures, we question the widely hold view that cluster magnetic fields may not be entirely of primordial origin.