Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale dependence, or running, of the density perturbation spectrum. We clarify the “universality classes” of inflation in this limit showing that a very small gravitational wave background can be correlated with a larger running. If pending experiments do not observe a gravitational wave background the running will be at the threshold of detectability if inflation is well described at third order in the slow-roll expansion.

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• Cosmic microwave background
• Inflation
• Large scale structure of the Universe