Strongly first order electroweak phase transition induced by primordial   hypermagnetic fields
  We consider the effect of the presence of a hypermagnetic field at the electroweak phase transition. Screening of the Z-component inside a bubble of the broken phase delays the phase transition and makes it stronger first order. We show that the sphaleron constraint can be evaded for m_H up to 100 GeV if a B_Y\gsim 0.3 T^2 exists at the time of the EW phase transition, thus resurrecting the possibility for baryogenesis within the minimal standard model (provided enough CP violation can be obtained). We estimate that for m_H\gsim 100 GeV the Higgs condendsate behaves like a type II superconductor with Z-vortices penetrating the bubble. Also, for such high Higgs masses the minimum B_Y field required for a strong first order phase transition is large enough to render the W-field unstable towards forming a condensate which changes the simple picture of the symmetry breaking. 
Per Elmfors, Kari Enqvist, Kimmo Kainulainen