In-in and $\delta N$ calculations of the bispectrum from non-attractor single-field inflation

TL;DR

This paper investigates the bispectrum in non-attractor single-field inflation models, demonstrating a consistent calculation of the local-form non-Gaussianity parameter across multiple methods, highlighting models that violate Maldacena's consistency relation.

Contribution

The paper provides a comprehensive calculation of the bispectrum in non-attractor inflation models using three different methods, confirming a large local non-Gaussianity for arbitrary sound speeds.

Findings

The bispectrum parameter is given by $f^{local}_{NL}=5(1+c_s^2)/(4c_s^2)$.

All three calculation methods agree on the bispectrum result.

Non-attractor models can produce large squeezed-limit bispectra violating Maldacena's relation.

Abstract

In non-attractor single-field inflation models producing a scale-invariant power spectrum, the curvature perturbation on super-horizon scales grows as ${\cal R}\propto a^3$. This is so far the only known class of self-consistent single-field models with a Bunch-Davies initial state that can produce a large squeezed-limit bispectrum violating Maldacena's consistency relation. Given the importance of this result, we calculate the bispectrum with three different methods: using quantum field theory calculations in two different gauges, and classical calculations (the $\delta N$ formalism). All the results agree, giving the local-form bispectrum parameter of $f^{local}_{NL}=5(1+c_s^2)/(4c_s^2)$. This result is valid for arbitrary values of the speed of sound parameter, $c_s$, for a particular non-attractor model we consider in this paper.