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

Maxim Dvornikov,Victor B Semikoz

doi:10.1140/epjc/s10052-021-09794-2

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.

Highlights

The origin of the baryon asymmetry of the Universe (BAU) is a long standing issue
The lepton asymmetry, in its turn, contributes the hypermagnetic fields evolution owing to the analog of the chiral magnetic effect [2]
We consider a novel scenario for the BAU generation in the symmetric phase in the early Universe, for which random hypermagnetic fields (HMFs), BY = 0, being small-scale at distances rD 10/T

Summary

Introduction

The origin of the baryon asymmetry of the Universe (BAU) is a long standing issue. One of the scenarios for the baryogenesis implies the production of a lepton asymmetry first. The goal of the present work is the study of the influence of the matter noise, or the turbulent motion of plasma, to the evolution of BAU and HMFs, both the HMF energy and the HMF helicity densities, in the symmetric phase before EWPT. 2, we consider the matter noise influence via Eq (1) for the spectra of HMF energy and helicity densities in the symmetric phase of the early Universe. 3, we reconsider the kinetic equations for the particle density asymmetries based on the first lepton generation in SM that are valid in the symmetric phase at T > TEWPT. The kinetic Eq (7) for the HMF spectra should be solved self-consistently with the evolution equations for the fermion density asymmetries in the background matter, η f (t) = n f (t) − n f(t)

Kinetic equations for the particle density asymmetries in the symmetric phase

Generation of the chiral imbalance in the symmetric phase

Complete set of the kinetic equations

Initial condition

Matter noise influences BAU and ξeR evolutions

Discussion