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