Reynolds numbers in the early Universe

Abstract

After electron-positron annihilation and prior to photon decoupling the magnetic Reynolds number is approximately twenty orders of magnitude larger than its kinetic counterpart which is, in turn, smaller than one. In this globally neutral system the large-scale inhomogeneities are provided by the spatial fluctuations of the scalar curvature. Owing to the analogy with the description of Markovian conducting fluids in the presence of acoustic fluctuations, the evolution equations of a putative magnetic field are averaged over the large-scale flow determined by curvature perturbations. General lessons are drawn on the typical diffusion scale of magnetic inhomogeneities. It is speculated that Reynolds numbers prior to electron-positron annihilation can be related to the entropy contained in the Hubble volume during the various stages of the evolution of the conducting plasma. © 2012 Elsevier B.V.