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

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 $$e_\mathrm {R,L}$$ e R , L and $$\nu _{e_\mathrm {L}}$$ ν e 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.

Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition

“…We vary B(0) Y in the range 1.4 × 10 −2 < B(0) Y < 1.4 × 10 −1 . Such HMFs contribute to neither the universe expansion nor the primordial nucleosynthesis [16].…”

“…(3.1) is chosen as ξ eL = ξ 0 = 0 and ξ eR = 10 −10 . Such values give the appropriate value of the observed BAU ∼ 10 −10 if this model is applied for this problem [16]. The initial spectra are Ẽ(0)…”

“…This model was studied in details in ref. [16] in connection to the BAU problem. The full set of the kinetic equations reads,…”

“…In ref. [16], we studied the influence of the HMF turbulence on the lepto-and baryogenesis in the early universe before EWPT. The noise of HMFs was modeled by the hypermagnetic hydrodynamics [(H)MHD] turbulence.…”

“…Now, if we apply the model in ref. [16] to describe the GWs production by the HMF turbulence, we will deal with the evolution of the spectra of the HMF energy density and helicity.…”