A new method for calculating the primordial bispectrum in the squeezed limit

TL;DR

This paper introduces a novel technique for calculating the primordial bispectrum in the squeezed limit, simplifying the process and testing the consistency relation across different inflation models without relying on slow-roll assumptions.

Contribution

Developed a new method based on the in-in formalism that simplifies the calculation of the squeezed-limit bispectrum without slow-roll approximation.

Findings

Validated the consistency relation for power-law inflation.

Found a non-zero bispectrum in the Starobinsky model, approaching zero in the long-wavelength limit.

Demonstrated the method's effectiveness beyond traditional slow-roll assumptions.

Abstract

In 2004, Creminelli and Zaldarriaga proposed a consistency relation for the primordial curvature perturbation of all single-field inflation models; it related the bispectrum in the squeezed limit to the spectral tilt. We have developed a technique, based in part on the Creminelli and Zaldarriaga argument, that can greatly simplify the calculation of the squeezed-limit bispectrum using the in-in formalism; we were able to arrive at a generic formula that does not rely on a slow-roll approximation. Using our formula, we explicitly tested the consistency relation for power-law inflation and for an exactly scale-invariant model by Starobinsky; for the latter model, Creminelli and Zaldarriaga's argument predicts a vanishing bispectrum whereas our quantum calculation shows a non-zero bispectrum that approaches zero in the long-wavelength limit and for inflation with a large number of e-folds.