The Separate Universe Approach to Soft Limits

TL;DR

This paper introduces a formalism using separate universe techniques to compute soft limits of inflationary correlation functions, accommodating multiple fields and deriving new consistency relations and inequalities.

Contribution

It develops a novel diagrammatic formalism for soft limits in multi-field inflation and generalizes existing inequalities between soft correlation functions.

Findings

Explicit formulas for all single- and double-soft limits of the trispectrum

Derivation of an infinite tower of inequalities generalizing Suyama-Yamaguchi

Enhanced understanding of consistency relations in multi-field inflation

Abstract

We develop a formalism for calculating soft limits of $n$-point inflationary correlation functions using separate universe techniques. Our method naturally allows for multiple fields and leads to an elegant diagrammatic approach. As an application we focus on the trispectrum produced by inflation with multiple light fields, giving explicit formulae for all possible single- and double-soft limits. We also investigate consistency relations and present an infinite tower of inequalities between soft correlation functions which generalise the Suyama-Yamaguchi inequality.