Magnetogenesis by non-minimal coupling to gravity in Higgs inflation model

Highlights: • We obtained modified potential in RCHI model which is valid for all stage of inflation in Higgs model. Eq. (52). • Showing that producing of magnetic field in this model is impossible (kinetic coupling) because it reduces to Starobinksky potential. • In Higgs model direct coupling to photon field is impossible. We used interaction term (25). This generates non-minimal coupling between gravity and electromagnetic field. • This theory does not contain ghost degrees of freedom. We study the generation of magnetic fields in the Higgs inflation model with the kinetic coupling in order to break the conformal invariance of the Maxwell action and produce strong magnetic fields. We consider radiatively corrected Higgs inflation potential. We assume that parity persevering non-minimal coupling between curvature and electromagnetic field is present in the action. In comparison to the Starobinsky potential, we obtain an extra term as a one loop correction and determine the spectrum of generalized electromagnetic fields. In this case it is impossible to produce large magnetic fields. Even for various values of coupling parameter $k_1$ it is obvious that the amplification of magnetic field is negligibly small. The reason is the nature of kinetic coupling and allowed values of inflationary anomalous scaling $A_I$. However, the effect of quantum correction in this case does not produce new dynamic for magnetogenesis but one may expect with axial coupling new dynamic can be produced by effect of quantum correction.