Generation of an electromagnetic field nonminimally coupled to gravity during Higgs inflation

In the framework of Higgs inflation, we consider electromagnetic field nonminimally coupled to gravity via parity-preserving $\propto RF^{2}$ and parity-violating RF\tilde{F}$ terms. Using perturbation theory leading order in these couplings, study generation during inflation stage. We derive effective kinetic axial coupling functions arising Einstein frame usual metric as well Palatini formulations gravity. For both formulations, determine power spectrum, energy density, helicality generated fields for different values nonminimal constants. Finally, estimate maximal present-day magnitude magnetic $10^{-14}-10^{-15}\,$G with correlation length 10 pc.