Rudenok I. Particles production, lepton asymmetry generation and magnetic fields evolution in the early Universe

Particles production rates on the stage of post-inflationary reheating in Starobinsky model are calculated. It was shown, that parametric resonance doesn't develop in such a model due to the universe expansion. Using the demand of sufficient lepton asymmetry for successful production of the Dark matter particles, the restrictions on the masses of sterile neutrinos and sterile-active neutrinos mixing angles in the neutrino SM modification are obtained. Using the chiral kinetic theory, expressions for the electric and chiral currents and charges and the equations for the electric and chiral chemical potentials in the chirally-asymmetric inhomogeneous early universe plasma are calculated. The evolution of the magnetic helicity in the chiral plasma is numerically simulated.The presence of the inverse cascade of magnetic helicity in the inhomogeneous plasma is established. It was shown that diffusion in the early universe causes sufficient suppression of the plasma inhomogeneities.