Impact of hypermagnetic fields on relic gravitational waves, neutrino
  oscillations and baryon asymmetry
  We study the evolution of random hypermagnetic fields (HMFs) in the symmetric
phase of the early universe before the electroweak phase transition. The
behavior of HMFs is driven by the analog of the chiral magnetic effect
accounting for the asymmetries of leptons and Higgs bosons. These asymmetries
are also dynamical variables of the model and evolve together with HMFs.
Moreover, we account for the contribution of the hyper-MHD turbulence in the
effective diffusion coefficient and the $\alpha$-dynamo parameter. The
realistic spectrum of seed HMFs consists of two branches: Batchelor and
Kolmogorov ones. The impact of HMFs on the production of relic gravitational
waves (GWs) and the baryon asymmetry of the universe (BAU), as well as flavor
oscillations of supernova neutrinos in the GWs generated are considered. We
establish the constraint on the strength of the seed HMF comparing the spectral
density of produced GWs with the observations of the LIGO-Virgo-KAGRA
collaborations. The stronger upper bound on the seed HMF is obtained from the
condition of not exceeding the observed value of BAU.
