The Physical Squeezed Limit: Consistency Relations at Order q^2

TL;DR

This paper investigates the physical effects of long-wavelength modes in single-field inflation models at order q^2, linking them to curvature effects and providing insights into non-Gaussianity levels.

Contribution

It verifies the physical influence of long modes at order q^2 in inflation, relating it to curvature effects and offering an alternative understanding of non-Gaussianity.

Findings

Long modes at order q^2 induce curvature effects similar to a curved universe.

Non-Gaussianity is parametrically enhanced when modes freeze at a physical scale shorter than H.

Order q^2 effects can be expressed in terms of the power spectrum in a curved universe.

Abstract

In single-field models of inflation the effect of a long mode with momentum q reduces to a diffeomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q^2 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 universe. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q^2 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 k_{ph, f} shorter than H: f_{NL} \sim (k_{ph, f}/H)^2.