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 the Ricci scalar and the Gauss-Bonnet invariant via the dual field tensor, so that the generated magnetic field can have a helical nature. It is demonstrated that if a reheating phase with non-zero e-fold numbers following inflation is taken into account, the energy density of the magnetic fields as well as their helicity spectrum evolve differently compared to those for the instantaneous reheating case. As a result, it is shown that in presence of the reheating phase, both the field strength of the generated magnetic fields and the resultant baryon asymmetry of the universe can be compatible with the observations. Furthermore, we find a viable constraint on the reheating equation of state parameter $\omega_\mathrm{eff}$ from the data of the cosmic microwave background radiation as $0.284 \lesssim \omega_\mathrm{eff} \lesssim 0.2975$, which is consistent with a negligible Schwinger backreaction.