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We study a matter turbulence caused by strong random hypermagnetic fields(HMFs ) that influence the baryon asymmetry evolution due to the Abeliananomalies in the symmetric phase in the early Universe. Such a matterturbulence is stipulated by the presence of the advection term in the inductionequation for which a fluid velocity is dominated by the Lorentz force in theNavier-Stokes equation. For random HMFs, having nonzero mean squared strengths,we calculate the spectra for the HMF energy and the HMF helicity densities. Thelatter function governs the evolution of the fermion asymmetries in thesymmetric phase before the electroweak phase transition (EWPT). In the simplestmodel 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 allfermion asymmetries including the baryon asymmetry, given by the `t Hooftconservation law, when one accounts for a turbulence of HMFs during theuniverse cooling down to EWPT. We obtain that the stronger the mean squaredstrength of random initial HMFs is, the deeper the fermion asymmetriesdecrease, compared to the case in the absence of any turbulence.

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