A universal bound on N-point correlations from inflation

TL;DR

This paper proves that the Suyama-Yamaguchi inequality relating three-point and four-point correlation functions in inflation models always holds, clarifying its applicability and interpretation in cosmological observations.

Contribution

We provide a general proof that the Suyama-Yamaguchi inequality is universally valid across inflation models, including specific scenarios like the ungaussiton model.

Findings

The inequality always holds, even in models suggesting potential violations.

Apparent violations in experiments can be explained by observational limitations.

The proof applies broadly to models with non-Gaussianity generated outside the horizon.

Abstract

Models of inflation in which non-Gaussianity is generated outside the horizon, such as curvaton models, generate distinctive higher-order correlation functions in the CMB and other cosmological observables. Testing for violation of the Suyama-Yamaguchi inequality tauNL >= (6/5 fNL)^2, where fNL and tauNL denote the amplitude of the three-point and four-point functions in certain limits, has been proposed as a way to distinguish qualitative classes of models. This inequality has been proved for a wide range of models, but only weaker versions have been proved in general. In this paper, we give a proof that the Suyama-Yamaguchi inequality is always satisfied. We discuss scenarios in which the inequality may appear to be violated in an experiment such as Planck, and how this apparent violation should be interpreted. We analyze a specific example, the "ungaussiton" model, in which leading-order scaling relations suggest that the Suyama-Yamaguchi inequality is eventually violated, and show that the inequality always holds.