Critical constraint on inflationary magnetogenesis
  Recently, there are several reports that the cosmic magnetic fields on Mpc
scale in void region is larger than $\sim 10^{-15}$G 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 $\rho_{\rm inf}^{1/4} <
30{\rm GeV} \times (B_{\rm obs}/10^{-15}{\rm G})^{-1}$ where $B_{\rm obs}$ 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.
