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Recently observational lower bounds on the strength of cosmic magnetic fieldswere reported, based on gamma-ray flux from distant blazars. If inflation isresponsible for the generation of such magnetic fields then the inflationenergy scale is bounded from above as rho_{inf}^{1/4} < 2.5 times 10^{-7}M_{Pl}times (B_{obs}/10^{-15}G)^{-2} in a wide class of inflationary magnetogenesismodels, where B_{obs} is the observed strength of cosmic magnetic fields. Thetensor-to-scalar ratio is correspondingly constrained as r< 10^{-19} times(B_{obs}/10^{-15}G)^{-8}. Therefore, if the reported strength B_{obs} \geq10^{-15}G is confirmed and if any signatures of gravitational waves frominflation are detected in the near future, then our result indicates sometensions between inflationary magnetogenesis and observations.

Universal upper limit on inflation energy scale from cosmic magnetic field