The (not so) squeezed limit of the primordial 3-point function

TL;DR

This paper proves that in single-field inflation models, the squeezed limit of the 3-point function has corrections that vanish quadratically with momentum ratio, and detecting deviations could rule out these models.

Contribution

It establishes that the consistency relation for the 3-point function in single-field models receives quadratic corrections, providing a new criterion to test these models against observations.

Findings

Corrections to the squeezed limit vanish as (k_L/k_S)^2.

Detection of a 1/k_L^2 bispectrum signal would rule out single-field models.

Scale dependence of bias at large scales would disprove all single-field models.

Abstract

We prove that, in a generic single-field model, the consistency relation for the 3-point function in the squeezed limit receives corrections that vanish quadratically in the ratio of the momenta, i.e. as (k_L/k_S)^2. This implies that a detection of a bispectrum signal going as 1/k_L^2 in the squeezed limit, that is suppressed only by one power of k_L compared with the local shape, would rule out all single-field models. The absence of this kind of terms in the bispectrum holds also for multifield models, but only if all the fields have a mass much smaller than H. The detection of any scale dependence of the bias, for scales much larger than the size of the haloes, would disprove all single-field models. We comment on the regime of squeezing that can be probed by realistic surveys.