Theory of Magnetic Seed-Field Theory of Magnetic Seed-Field Generation
  during the Cosmological First-Order Electroweak Phase Transition
  We present a theory of the generation of magnetic seed fields in bubble
collisions during a first-order electroweak phase transition (EWPT) possible
for some choices of parameters in the minimal supersymmetric Standard Model.
The theory extends earlier work and is formulated to assess the importance of
surface dynamics in such collisions. We are led to linearized equations of
motion with O(3) symmetry appropriate for examining collisions in which the
Higgs field is relatively unperturbed from its mean value in the collision
volume. Coherent evolution of the charged $W$ fields within the bubbles is the
main source of the electromagnetic current for generating the seed fields, with
fermions also contributing through the conductivity terms. We present numerical
simulations within this formulation to quantify the role of the surface of the
colliding bubbles, particularly the thickness of the surface, and to show how
conclusions drawn from earlier work are modified. The main sensitivity arises
such that the steeper the bubble surface the more enhanced the seed fields
become. Consequently, the magnetic seed fields may be several times larger and
smoother over the collision volume than found in earlier studies. Our work thus
provides additional support to the supposition that magnetic fields produced
during the EWPT in the early universe seed the galactic and extra-galactic
magnetic fields observed today.
