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 enough magnetic fields for observed large-scale magnetic fields. This interaction breaks the parity and enables a production of only one of the polarization states of the electromagnetic field due to axion-like coupling of electromagnetic field to the inflation. Therefore, the produced magnetic fields are helical. In fact,calculations show the mode of one polarization undergoes amplification, while the other one diminishes. 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. The effect of quantum correction modifies potential so that in some certain conditions when back reaction is weak the observed large-scale magnetic field can be explained by our modified potential. We should emphasize in this model we only consider linear approximation for electromagnetic field so that the theory does not contain higher-order derivatives and the so-called ghost degrees of freedom. Therefore, the theory is consistent with cosmology. In addition,the magnetic field generated in this model has very small correlation length. It is impossible to explain within this model both the strength of magnetic field and its large coherence length. Due to the nontrivial helicity, the produced magnetic fields undergo the inverse cascade process in the turbulent plasma which can strongly increase their correlation length. We find that, for two values of coupling parameter chi(1) = 5 x 10(9) M-p(-2) and chi(1) = 7.5 x 10(9) M-p(-2) , the back-reaction is weak and our analysis is valid.