Critical constraint on inflationary magnetogenesis

Recently, there are several reports that the cosmic magnetic fields on Mpc scale in void region is larger than ∼ 10^-15G with an uncertainty of a few orders from the current blazar observations. On the other hand, in inflationary magnetogenesis models, additional primordial curvature perturbations are inevitably produced from iso-curvature perturbations due to generated electromagnetic fields. We explore such induced curvature perturbations in a model independent way and obtained a severe upper bound for the energy scale of inflation from the observed cosmic magnetic fields and the observed amplitude of the curvature perturbation , as ρinf^1/4 < 300MeV × (Bobs/10^-15G)^-1 where Bobs is the strength of the magnetic field at present. Therefore, without a dedicated low energy inflation model or an additional amplification of magnetic fields after inflation, inflationary magnetogenesis on Mpc scale is generally incompatible with CMB observations.