Universal upper limit on inflation energy scale from cosmic magnetic field

Recently observational lower bounds on the strength of cosmic magnetic fields were reported, based on γ-ray flux from distant blazars. If inflation is responsible for the generation of such magnetic fields then the inflation energy scale is bounded from above as ρ inf 1/4 < 2.5 × 10 −7 M Pl × ( B obs /10 −15 G) −2 in a wide class of inflationary magnetogenesis models, where B obs is the observed strength of cosmic magnetic fields. The tensor-to-scalar ratio is correspondingly constrained as r < 10 −19 × ( B obs /10 −15 G) −8 . Therefore, if the reported strength B obs ⩾ 10 −15 G is confirmed and if any signatures of gravitational waves from inflation are detected in the near future, then our result indicates some tensions between inflationary magnetogenesis and observations.