The Inflationary Wavefunction from Analyticity and Factorization

TL;DR

The paper develops a tree-level bootstrap for inflationary wavefunction coefficients in quasi-de Sitter space with boost-breaking interactions, deriving cutting rules and dispersion relations from the analyticity of bulk propagators. This framework allows one to reconstruct higher-point wavefunction coefficients from lower-point data, demonstrated across four-, five-, and all-order EFT of inflation scenarios, with explicit four-point and five-point examples. It also shows that these dS results are connected to AdS techniques through analytic continuation, clarifying the holographic perspective. The work sets the stage for extensions to loops, spinning operators, and more general spacetimes, with potential to constrain inflationary UV completions using causality and unitarity.

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.