Contribution of the chiral vortical effect to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the early Universe

In this paper, we study the contribution of the chiral vortical effect, in addition to that of the chiral magnetic effect, to the evolution of the hypermagnetic field and the matter-antimatter asymmetry in the symmetric phase of the early Universe in the temperature range 100 GeV <= T <= 10 TeV. We choose a fully helical Chem-Simons wave configuration for the velocity and the hypermagnetic vector potential fields. The latter makes the plasma forcefree in the absence of viscosity. We show that the most pronounced effect of the chiral vorticity is the production and initial growth of the hypermagnetic field. In particular, we show that in the presence of a nonzero matter asymmetry, the hypermagnetic field can grow from zero initial value only in the presence of a nonzero vorticity field. Moreover, we show that larger initial growths not only result in larger maximum values of the hypermagnetic field, but also cause the saturation of the hypermagnetic field and the conversion of the lepton-baryon asymmetry to occur more quickly, i.e., at a higher temperature. We show that the damping of the vorticity due to the presence of viscosity, which typically occurs extremely rapidly, does not significantly affect the evolution.