The physical squeezed limit: consistency relations at order<i>q</i>²

Abstract

In single-field models of inflation the effect of a long mode with momentum q reduces to a dif-feomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW uni-verse. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale kph, f shorter than H: fNL ∼ (kph, f/H)2. 1 Introduction and main results In single-field inflation, correlation functions of the curvature perturbation ζ and of tensor modes satisfy general, model-independent relations in the limit in which one of the momenta (or the sum of some of the momenta) becomes very small compared to the others: the so-called consistency relations [1–9]. Physically, they are based on the observation that the effect of a long mode on the