Estimate of a non-helical electroweak primordial bootstrap field today

Abstract: We estimate the magnitude today of the primordial magnetic field originating at the electroweak phase transition. We find that the field, which at the electroweak phase transition is originally of order $10^{23}-10^{24}$ G correlated over the Hubble scale, today is of order $10^{-14}$ G at a scale of order 2 kpc. This result is consistent with the lower limit on the strength of intergalactic magnetic fields obtained by Neronov and Vovk from observations of TeV blazars. The field is non-helical. We compare our results with the helical case discussed by Field and Carroll.