Theory of Magnetic Seed-Field Theory of Magnetic Seed-Field Generation during the Cosmological First-Order Electroweak Phase Transition

TL;DR

This paper develops a detailed theory and numerical simulations for magnetic seed field generation during a first-order electroweak phase transition, emphasizing the role of bubble surface dynamics and their impact on seed field strength.

Contribution

It extends previous models by incorporating surface dynamics and provides quantitative analysis showing how bubble surface steepness enhances seed magnetic fields.

Findings

Steeper bubble surfaces lead to stronger seed magnetic fields.

Seed fields generated can be several times larger than previous estimates.

Surface thickness significantly influences the magnitude and smoothness of seed fields.

Abstract

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.