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We study the evolution of hypermagnetic fields (HMFs) in random plasma in thesymmetric phase of the early universe. The system of kinetic equations for thespectra of the energy density and the helicity, as well as the particlesasymmetries is derived. We also formulate the initial condition which involvethe Kazantsev and Kolmogorov spectra of the seed HMFs. This system is solvednumerically. We predict the energy spectrum of primeval gravitational waveswhich are produced by these HMFs. Additionally, the baryon asymmetry of theuniverse, generated by the lepton asymmetries, is obtained. These results allowus to constrain the strength of seed HMFs.

Production of relic gravitational waves and the baryon asymmetry of the universe by random hypermagnetic fields