Helical magnetogenesis with reheating phase from higher curvature coupling and baryogenesis

We investigate the generation of helical magnetic fields and address the baryon asymmetry of the universe from an inflationary magnetogenesis scenario, in which the conformal and parity symmetries of the electromagnetic field are broken through its coupling to the Ricci scalar and to the Gauss-Bonnet invariant via the dual field tensor, so that the generated magnetic field can have a helical nature. Depending on the reheating mechanism, we consider two different cases - (1) instantaneous reheating scenario, in which case the reheating e-fold number is zero, and (2) Kamionkowski reheating scenario which is parametrized by a non-zero e-fold number, a reheating equation of state parameter and a given reheating temperature. It is demonstrated that for both the reheating mechanisms, the generated magnetic fields can be compatible with the observations for suitable range of the model parameter present in the non-minimal coupling of the electromagnetic field. Actually the present magnetogenesis model does not produce sufficient hierarchy between the electric and magnetic fields at the end of inflation, and thus the electric field is not able to sufficiently induce (or enhance) the magnetic field during the Kamionkowski reheating stage. This in turn makes both the reheating cases almost similar from the perspective of magnetic field's evolution. Furthermore we find that the magnetic fields at the galactic scale with strength $\sim 10^{-13}\mathrm{G}$ can lead to the resultant value of the ratio of the baryonic number density to the entropy density as large as $\sim 10^{-10}$, which is consistent with the observational data.