Can Electric Charges and Currents Survive in an Inhomogeneous Universe?
  Although observations point to the neutrality and lack of currents on large scales in the universe, many mechanisms are known that can generate charges or currents during the early universe. We examine the question of survivability of relic charges and currents in a realistic model of the universe. We show that the dynamics of cosmological perturbations drive the universe to become electrically neutral and current-free to a high degree of accuracy on all scales, regardless of initial conditions. We find that charges are efficiently driven away in a time small compared to the Hubble time for temperatures 100 GeV > T > 1 eV, while the same is true for currents at all temperatures T > 1 eV. The forced neutrality relaxes constraints on the generation of an electric charge in the early universe, while the forced erasure of currents disfavors many mechanisms for the early origins of large-scale magnetic fields. 
E. R. Siegel, J. N. Fry