Extension of local-type inequality for the higher order correlation functions

TL;DR

This paper develops a systematic formalism using diagrammatic methods to derive inequalities between higher-order correlation functions in local-type primordial perturbations, extending known bispectrum-trispectrum inequalities to six- and eight-point functions.

Contribution

It introduces a general formalism for constructing inequalities among any order correlation functions, expanding the understanding of primordial perturbation constraints.

Findings

Derived inequalities up to six- and eight-point functions.

Established a systematic diagrammatic approach for higher-order correlations.

Extended the known bispectrum-trispectrum inequality to higher orders.

Abstract

For the local-type primordial perturbation, it is known that there is an inequality between the bispectrum and the trispectrum. By using the diagrammatic method, we develop a general formalism to systematically construct the similar inequalities up to any order correlation function. As an application, we explicitly derive all the inequalities up to six and eight-point functions.