Non-Gaussianity Consistency Relation for Multi-field Inflation

TL;DR

This paper derives a new inequality relating the local non-Gaussianity parameters in multi-field inflation models, which can be tested observationally to distinguish between single-field and multi-field inflation scenarios.

Contribution

It establishes a novel inequality between $f_{NL}$ and $ au_{NL}$ in multi-field inflation models using the $ abla$ formalism, providing a new observational test.

Findings

The inequality $ au_{NL}>rac12(rac65f_{NL})^2$ holds for most multi-field models.

Violation of this inequality would rule out many multi-field inflation models.

The relation includes possible logarithmic scale dependence.

Abstract

While detection of the "local form" bispectrum of primordial perturbations would rule out all single-field inflation models, multi-field models would still be allowed. We show that multi-field models described by the $\delta N$ formalism obey an inequality between $f_{\rm NL}$ and one of the local-form {\it trispectrum} amplitudes, $\tau_{\rm NL}$, such that $\tau_{\rm NL}>\frac12(\frac65f_{\rm NL})^2$ with a possible logarithmic scale dependence, provided that 2-loop terms are small. Detection of a violation of this inequality would rule out most of multi-field models, challenging inflation as a mechanism for generating the primoridal perturbations.