On the consistency relation of the 3-point function in single field inflation

TL;DR

The work addresses whether the Maldacena consistency relation for the squeezed-limit three-point function holds for all single-clock (single-field) inflation models. It develops and employs an effective field theory of inflation to perform an explicit verification across representative models, including k-inflation and ghost-condensate-like regimes, up to leading and next-to-leading slow-roll orders. The main finding is that the squeezed-limit three-point function is determined by the power spectrum tilt of the short mode, ensuring the consistency relation is preserved across the tested single-clock theories. This explicit, model-independent validation strengthens the theoretical basis for ruling out single-field inflation if a detectable squeezed non-Gaussian signal is observed in future cosmic microwave background measurements.

Abstract

The consistency relation for the 3-point function of the CMB is a very powerful observational signature which is believed to be true for every inflationary model in which there is only one dynamical degree of freedom. Its importance relies on the fact that deviations from it might be detected in next generation experiments, allowing us to rule out all single field inflationary models. After making more precise the already existing proof of the consistency relation, we use a recently developed effective field theory for inflationary perturbations to provide an alternative and very explicit proof valid at leading non trivial order in slow roll parameters.