Scalar Bispectrum Beyond Slow-Roll in the Unified EFT of Inflation

TL;DR

This paper develops a comprehensive framework for calculating the scalar bispectrum in the unified EFT of inflation, valid beyond slow-roll conditions, and demonstrates its accuracy in a transitioning inflation model.

Contribution

It provides the first complete formulation of the scalar bispectrum within the unified EFT of inflation, including beyond-Horndeski theories, valid during transient slow-roll violations.

Findings

Explicitly preserves the squeezed-limit consistency relation beyond slow-roll

Accurately tracks the bispectrum during slow-roll violations in a transitioning inflation model

Provides simple integral expressions applicable to all bispectrum configurations

Abstract

We present a complete formulation of the scalar bispectrum in the unified effective field theory (EFT) of inflation, which includes the Horndeski and beyond-Horndeski Gleyzes-Langlois-Piazza-Vernizzi classes, in terms of a set of simple one-dimensional integrals. These generalized slow-roll expressions remain valid even when slow-roll is transiently violated and encompass all configurations of the bispectrum. We show analytically that our expressions explicitly preserve the squeezed-limit consistency relation beyond slow-roll. As an example application of our results, we compute the scalar bispectrum in a model in which potential-driven G-inflation at early times transitions to chaotic inflation at late times, showing that our expressions accurately track the bispectrum when slow-roll is violated and conventional slow-roll approximations fail.