Primordial magnetic field and kinetic theory with Berry curvature

We study the generation of a magnetic field in primordial plasma of standard model particles at a temperature T>80 TeV - much higher than the electroweak scale. It is assumed that there is an excess number of right-handed electrons compared to left-handed positrons in the plasma. Using the Berry-curvature modified kinetic theory to incorporate the effect of the Abelian anomaly, we show that this chiral imbalance leads to the generation of a hypermagnetic field in the plasma in both the collision dominated and collisionless regimes. It is shown that, in the collision dominated regime, the chiral-vorticity effect can generate finite vorticity in the plasma together with the magnetic field. Typical strength of the generated magnetic field is 1027 G at T∼80 TeV with the length scale 105/T, whereas the Hubble length scale is 1013/T. Furthermore, the instability can also generate a magnetic field of the order 1031 G at a typical length scale 10/T. But there may not be any vorticity generation in this regime. We show that the estimated values of the magnetic field are consistent with the bounds obtained from current observations.