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.