Influence of the hypermagnetic field noise on the baryon asymmetry generation in the symmetric phase of the early universe

TL;DR

This paper investigates how strong random hypermagnetic fields in the early universe's symmetric phase induce turbulence that affects the evolution and reduction of fermion and baryon asymmetries before the electroweak phase transition.

Contribution

It introduces a model linking hypermagnetic field turbulence with fermion asymmetry evolution, highlighting the impact of turbulence strength on asymmetry decline.

Findings

Stronger hypermagnetic turbulence leads to greater reduction of fermion asymmetries.

Calculated spectra for hypermagnetic energy and helicity densities.

Fermion asymmetries decrease more significantly with increased initial hypermagnetic field strength.

Abstract

We study a matter turbulence caused by strong random hypermagnetic fields (HMFs ) that influence the baryon asymmetry evolution due to the Abelian anomalies in the symmetric phase in the early Universe. Such a matter turbulence is stipulated by the presence of the advection term in the induction equation for which a fluid velocity is dominated by the Lorentz force in the Navier-Stokes equation. For random HMFs, having nonzero mean squared strengths, we calculate the spectra for the HMF energy and the HMF helicity densities. The latter function governs the evolution of the fermion asymmetries in the symmetric phase before the electroweak phase transition (EWPT). In the simplest model based on the first SM generation for the lepton asymmetries of $e_\mathrm{R,L}$ and $\nu_{e_\mathrm{L}}$, we calculate a decline of all fermion asymmetries including the baryon asymmetry, given by the `t Hooft conservation law, when one accounts for a turbulence of HMFs during the universe cooling down to EWPT. We obtain that the stronger the mean squared strength of random initial HMFs is, the deeper the fermion asymmetries decrease, compared to the case in the absence of any turbulence.