Are cluster magnetic fields primordial?

We present results of a detailed and fully nonlinear 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) G on comparatively small scales 100 pc-10 kpc may survive to the present. Building on prior numerical work on the evolution of magnetic fields during the course of gravitational collapse of a cluster, which indicates that precollapse fields of similar to4x10(-12) G extant on small scales may suffice to produce clusters with acceptable Faraday rotation measures, we argue that it seems possible for cluster magnetic fields to be entirely of primordial origin.