On Graviton non-Gaussianities in the Effective Field Theory of Inflation

TL;DR

This paper derives all possible graviton bispectra in the Effective Field Theory of Inflation, revealing the dominant operators and providing compact expressions for boundary correlators, advancing understanding of primordial gravitational non-Gaussianities.

Contribution

It systematically constructs and analyzes graviton bispectra in EFToI to all derivative orders, identifying key operators and simplifying the calculation of boundary correlators.

Findings

All relevant cubic operators involve extrinsic curvature and derivatives.

Boundary correlators are surprisingly compact despite complex bulk interactions.

Single exchange diagrams have only total-energy poles and satisfy the Manifestly Local Test.

Abstract

We derive parity-even graviton bispectra in the Effective Field Theory of Inflation (EFToI) to all orders in derivatives. Working in perturbation theory, we construct all cubic interactions that can contribute to tree-level graviton bispectra, showing that they all come from EFToI operators containing two or three powers of the extrinsic curvature and its covariant derivatives: all other operators can be removed by field redefinitions or start at higher-order in perturbations. For operators cubic in the extrinsic curvature, where the single-clock consistency relations are satisfied without a correction to the graviton two-point function, we use the Manifestly Local Test (MLT) to efficiently extract the effects of evolving graviton fluctuations to the end of inflation. Despite the somewhat complicated nature of the bulk interactions, the final boundary correlators take a very compact form. For operators quadratic in the extrinsic curvature, the leading order bispectra are a sum of contact and single exchange diagrams, which are tied together by spatial diffeomorphisms, and to all orders in derivatives we derive these bispectra by computing the necessary bulk time integrals. For single exchange diagrams we exploit factorisation properties of the bulk-bulk propagator for massless gravitons and write the result as a finite sum over residues. Perhaps surprisingly, we show these single exchange contributions have only total-energy poles and also satisfy the MLT.