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 -7M Pl × (B obs/10 -15G) -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 -15G) -8. Therefore, if the reported strength B obs 10 -15G 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.
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