Origin and dynamics of the Primordial Magnetic field in a parity violating plasma

In this thesis, we have studied the generation and evolution of the magnetic field in the early Universe. We investigated the generation of magnetic fields in the presence of chiral symmetry and gravitational anomaly. We have used modified kinetic theory by Berry curvature and derived expressions for magnetic and vortical conductivities. We have also shown that there are two length scales: kinetic and viscous, which is one of the important results. In the latter part of the thesis, we have shown the effect of second-order viscous effects on the modes of the magnetic fields.