Primordial magnetic field and kinetic theory with Berry curvature

We apply the modified kinetic theory to study generation of magnetic field due to anomaly in a primordial plasma of the standard model particles at temperature T >80 TeV. It is known that achiral imbalance in such plasma can lead to instabilities responsible for the origin of the magneticfields. We have shown that inclusion of the Berry curvature term in the kinetic equation alongwith the collision term in the ralaxation approximation canlead to the chiral vorticity effect. Thiseffect was not considered in the earlier literature based on the heuristic application of the kinetictheory. But in the collisionless regime there may not be any vorticity generation. We also arguedthat the chiral imbalance in the collisionless regime remains subdominant for the primordial plasmacompared to the case where the collisions are important.