Impact of Primordial Magnetic Fields on the First-Order Electroweak Phase Transition

We numerically study how the primordial magnetic field affects the first-order electroweak phase transition in the early Universe. We observe that: 1) the phase transition process would be slowed down by the magnetic field; 2) the phenomenon of vortex structure of the Higgs condensation appears when the homogenesis hypermagentic field $g^{\mathrm{\prime }}{B}_Y^{ex}\mathrm{/}{m}_W^2\gtrsim 3.63$; and, 3) the helical hypermagnetic field can dramatically enhance the sphaleron rate and validate the generation of the baryon asymmetry through the chiral anomaly.