Born to Run: Inflationary Dynamics and Observational Constraints
  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 "equivalence classes" of
inflationary models in this limit, showing that models with a very small
gravitational wave background typically have a larger running and that if this
background is not observed by pending experiments the running could be at the
threshold of detectability. Correlated expectations for the running and
gravitational wave background provide an new avenue by which future
observations may yield insight into possible inflationary mechanisms.
