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 the following: 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msup> <a:mrow> <a:mi>g</a:mi> </a:mrow> <a:mrow> <a:mo>′</a:mo> </a:mrow> </a:msup> <a:msubsup> <a:mrow> <a:mi>B</a:mi> </a:mrow> <a:mrow> <a:mi>Y</a:mi> </a:mrow> <a:mrow> <a:mi>e</a:mi> <a:mi>x</a:mi> </a:mrow> </a:msubsup> <a:mo>/</a:mo> <a:msubsup> <a:mrow> <a:mi>m</a:mi> </a:mrow> <a:mrow> <a:mi>W</a:mi> </a:mrow> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:msubsup> <a:mo>≳</a:mo> <a:mn>3.63</a:mn> </a:mrow> </a:math> ; and, 3) the helical hypermagnetic field can dramatically enhance the sphaleron rate and validate the generation of the baryon asymmetry through the chiral anomaly.