Squeezed Bispectrum in the $\delta N$ Formalism: Local Observer Effect in Field Space

TL;DR

This paper introduces a new method using the $ abla$ formalism to compute the squeezed bispectrum in multi-field inflation, clarifying local observer effects and including intrinsic non-Gaussianities, with applications to future galaxy surveys.

Contribution

It presents a novel $ abla$ formalism approach for calculating the squeezed bispectrum in multi-field inflation, accounting for local observer effects and intrinsic non-Gaussianities.

Findings

Squeezed bispectrum vanishes in single-field inflation for local observers.

The method works beyond the small hierarchy limit.

Intrinsic non-Gaussianities are automatically included.

Abstract

The prospects of future galaxy surveys for non-Gaussianity measurements call for the development of robust techniques for computing the bispectrum of primordial cosmological perturbations. In this paper, we propose a novel approach to the calculation of the squeezed bispectrum in multiple-field inflation. With use of the $\delta N$ formalism, our framework sheds new light on the recently pointed out difference between the squeezed bispectrum for global observers and that for local observers, while allowing one to calculate both. For local observers in particular, the squeezed bispectrum is found to vanish in single-field inflation. Furthermore, our framework allows one to go beyond the near-equilateral ("small hierarchy") limit, and to automatically include intrinsic non-Gaussianities that do not need to be calculated separately. The explicit computational programme of our method is given and illustrated with a few examples.