Classical issues in electroweak baryogenesis

TL;DR

This paper models electroweak baryogenesis during a cold transition, using classical simulations of the Higgs field's tachyonic instability and CP-violation to compute the resulting matter-antimatter asymmetry.

Contribution

It introduces a classical real-time simulation approach to electroweak baryogenesis, avoiding lattice difficulties by modeling the transition with a sign change in the Higgs mass parameter.

Findings

Rapid growth of occupation numbers during the transition

Classical approximation effectively captures baryon asymmetry

CP-violation influences the generated Chern-Simons number

Abstract

In one scenario of baryogenesis, the matter-antimatter asymmetry was generated in the early universe during a cold electroweak transition. We model this transition by changing the sign of the effective mass-squared parameter of the Higgs field from positive to negative. The resulting `tachyonic' instability leads to a rapid growth of occupation numbers, such that a classical approximation can be made in computing subsequent developments in real time. We solve the classical equations of motion in the SU(2)-Higgs model under the influence of effective CP-violation. The resulting baryon asymmetry follows from the generated Chern-Simons number using the anomaly equation. The `classical' difficulties with lattice implementations of these observables are avoided here because the fields are smooth on the lattice scale.