Consistency Relations for Non-Gaussianity

TL;DR

The paper provides a model-independent, dynamical proof of consistency relations for primordial non-Gaussianity, derived from the Hamiltonian and from local field redefinitions, and shows these relations hold for the squeezed limit of the 3-point function as well as for general $n$-point functions to arbitrary perturbative order and loop level. It demonstrates explicit applications to single-field inflation with canonical and generalized kinetic terms, to multi-field inflation, and to the curvaton scenario, including how a local field redefinition contributes to non-Gaussianity. The framework unifies how long-wavelength modes modulate short-scale correlations and extends Maldacena’s results to broader contexts via a background-derivative structure and a general redefinition formalism. This approach provides a robust theoretical tool for validating calculations and interpreting non-Gaussianity measurements across inflationary models.

Abstract

We investigate consistency relations for non-Gaussianity. We provide a model-independent dynamical proof for the consistency relation of 3-point correlation functions from the Hamiltonian and field redefinition. This relation can be applied to single field inflation, multi-field inflation and the curvaton scenario. This relation can also be generalized to $n$-point correlation functions up to arbitrary order in perturbation theory and with arbitrary number of loops.