Non-Abelian Higgs model of magnetic field generation during a cosmological first-order electroweak phase transition

Abstract

We present a theory of the generation of magnetic fields in bubble collisions during the electroweak phase transition, which may be first order in various extensions of the standard model, for example, the minimal supersymmetric standard model. Using the equations of motion determined from an effective minimal supersymmetric standard model Lagrangian, we derive the magnetic field using a model of gentle collisions of the electroweak phase transition bubbles, discussed in our earlier work. Solutions of the relevant equations of motion for the magnetic field are examined in O(1,2) space-time symmetry with boundary conditions applied at the time of collision. These solutions indicate that the magnetic fields evolving from our equations of motion are somewhat larger in magnitude and extend more uniformly through the available volume of the bubble than those found in the Abelian Higgs model. The magnetic fields so produced might possibly seed galactic and extragalactic magnetic fields observed today.