Magnetogenesis in Higgs inflation

We study the generation of magnetic fields in the Higgs inflation model with the axial coupling in order to break the conformal invariance of the Maxwell action and produce strong magnetic fields. We consider radiatively corrected Higgs inflation potential. In comparison to the Starobinsky potential, we obtain an extra term as a one loop correction and determine the spectrum of generalized electromagnetic fields. For two values of coupling parameter $\chi_{1}=5\times 10^{9}$ and $\chi_{1}=7.5\times 10^{9}$, the back-reaction is weak and our analysis is self-consistent.