The Separate Universe Approach to Soft Limits

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.

28 pages, 7 figures. This is an author-created, un-copyedited version of an article published in JCAP. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at the DOI below. v3: Updated to match version published in JCAP

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• Non-Gaussianity in two-field inflation beyond the slow-roll approximation
• The scalar-scalar-tensor inflationary three-point function in the axion monodromy model
• The Size of Local Bispectrum and Trispectrum in a Non-Minimal Inflation
• Squeezed bispectrum from multi-field inflation with curved field space metric
• Non-Gaussianity after many-field reheating
• Non-Gaussianity in D3-brane inflation
• Non-Gaussianity in Cosmology: from Inflation to the CMB