Extragalactic magnetic fields unlikely generated at the electroweak phase transition

Abstract

In this letter we show that magnetic fields generated at the electroweak phase transition are most likely too weak to explain the void magnetic fields apparently observed today unless they have considerable helicity. We show that, in the simplest estimates, the helicity naturally produced in conjunction with the baryon asymmetry is too small to explain observations, which require a helicity fraction at least of order $10^{-14}-10^{-10}$ depending on the void fields constraint used. Therefore new mechanisms to generate primordial helicity are required if magnetic fields generated during the electroweak phase transition should explain the extragalactic fields.