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

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 2 L 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.

Inflationary consistency conditions from a wavefunctional perspective

“…One can check that changing variables from k 2 to k S such is the case, so (5.23) is compatible with the claims made in [6,7]. We can also study the case of one long tensor mode and two short scalar modes, as in [7].…”

“…Considerable progress has been made since, by several groups, on studying subleading corrections to the squeezed limit. Also, consistency conditions coming from soft internal momenta were found, relevant to squeezed limits of expectation values with four or more legs [5][6][7][8][9][10][11]. The derivations attack the problem from various perspectives.…”

Non-Gaussianity as a particle detector

“…The consistency condition furthermore fixes the coefficient of the linear term, b 1 , and partially constrains higher-order coefficients [41][42][43][44][45][46]. Since the contributions coming from b 0 and b 1 cannot be measured by a local observer [47,48], any physical effect will only appear at order (k 1 /k 3 ) 2 [49]. A crucial consequence of the consistency relation is the existence of the Taylor expansion (4.16) with only integer powers of k 1 /k 3 .…”

Effects and detectability of quasi-single field inflation in the large-scale structure and cosmic microwave background

“…0 ≤ ν ≤ 3/2. Such a momentum dependence lies between that of the equilateral shape (α = 1) which arises in single field models with large non-Gaussianity or its direct multifield generalization, and that of the local shape (α = −1) which arises in multifield models with light isocurvatons m H (see [6,60,61] for reviews. )…”