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

TL;DR

This paper refines the proof of the single-field inflationary consistency relation for the 3-point function of the CMB, emphasizing its importance for testing inflation models with upcoming experiments.

Contribution

It provides a more precise and explicit proof of the consistency relation using effective field theory, valid at leading order in slow roll parameters.

Findings

The consistency relation holds under more precise conditions.

Effective field theory offers a clear proof at leading slow roll order.

Deviations from the relation could rule out single-field inflation.

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.