Primordial magnetic fields and gravitational baryogenesis in nonlinear electrodynamics

The amplification of the primordial magnetic fields and the gravitational baryogenesis, a mechanism that allows one to generate the baryon asymmetry in the Universe by means of the coupling between the Ricci scalar curvature and the baryon current, are reviewed in the framework of the nonlinear electrodynamics. To study the amplification of the primordial magnetic field strength, we write down the gauge invariant wave equations and then solve them (in the long wavelength approximation) for three different eras of the Universe: de Sitter, the reheating, and the radiation-dominated era. Constraints on parameters entering the nonlinear electrodynamics are obtained by using the amplitude of the observed galactic magnetic fields and the baryon asymmetry, which are characterized by the dimensionless parameters $r\sim {10}^{-37}$ and ${\eta }_B\lesssim 9\times {10}^{-11}$, respectively.