The Inflationary Wavefunction from Analyticity and Factorization

TL;DR

This paper develops a unitarity-based method using analyticity and factorization to compute inflationary wavefunction coefficients, especially for theories breaking de Sitter boost symmetry, enabling efficient calculation of non-Gaussianities.

Contribution

It introduces cutting rules and dispersion formulas for wavefunction coefficients in quasi-de Sitter space, applicable to arbitrary mass fields and n-point functions, advancing the computational framework for inflationary correlators.

Findings

Derived unitarity-based cutting rules for wavefunction coefficients

Expressed boost-breaking exchange diagrams as finite sums over residues

Connected dS identities to Anti-de Sitter space via analytic continuation

Abstract

We study the analytic properties of tree-level wavefunction coefficients in quasi-de Sitter space. We focus on theories which spontaneously break dS boost symmetries and can produce significant non-Gaussianities. The corresponding inflationary correlators are (approximately) scale invariant, but are not invariant under the full conformal group. We derive cutting rules and dispersion formulas for the late-time wavefunction coefficients by using factorization and analyticity properties of the dS bulk-to-bulk propagator. This gives a unitarity method which is valid at tree-level for general $n$-point functions and for fields of arbitrary mass. Using the cutting rules and dispersion formulas, we are able to compute $n$-point functions by gluing together lower-point functions. As an application, we study general four-point, scalar exchange diagrams in the EFT of inflation. We show that exchange diagrams constructed from boost-breaking interactions can be written as a finite sum over residues. Finally, we explain how the dS identities used in this work are related by analytic continuation to analogous identities in Anti-de Sitter space.