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

TL;DR

This work develops a general, slow-roll–independent method to compute the squeezed-limit primordial bispectrum using the in-in formalism. By splitting the curvature perturbation into long- and short-wavelength components and carefully integrating out the short modes, the authors derive a compact formula for the squeezed bispectrum in terms of mode functions and a single time-integral, without assuming slow-roll. They verify the standard single-field consistency relation in slow-roll and power-law inflation and reveal finite-duration-inflation corrections in Starobinsky’s exactly scale-invariant model, clarifying the conditions under which the relation holds. The approach also connects to the $\delta N$ formalism via a field-redefinition term and offers a framework extendable to non-standard kinetic terms and higher-point functions, with implications for interpreting constraints on primordial non-Gaussianity.

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.