Running primordial perturbations: Inflationary Dynamics and Observational Constraints

TL;DR

This paper investigates how constraints from inflation duration and gravitational wave bounds influence the inflaton potential's derivatives, affecting the spectrum's scale-dependence and running, with implications for upcoming observations.

Contribution

It demonstrates that higher derivatives of the inflaton potential are nontrivial under current constraints, linking gravitational wave background levels to the running of density perturbations.

Findings

Higher derivatives of the potential are significant with 99% confidence.

Small gravitational wave background can be associated with larger running.

Running may be detectable if inflation is described by third-order slow roll expansion.

Abstract

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.