Cosmological Cutting Rules from Flat-Space Unitarity via Dressing

TL;DR

This paper develops a direct, diagram-by-diagram route to cosmological cutting rules by dressing flat-space unitarity cuts and analytically continuing to de Sitter and EAdS backgrounds. The main idea is that Cutkosky delta functions uplift to Disc operations in the exchanged energy variable once the flat-space amplitude is dressed, enabling a transparent translation from flat-space unitarity to cosmological discontinuity relations. The authors illustrate the dictionary with explicit tree-level and one-loop examples for conformally coupled scalars, deriving both the tree-level factorization and loop-level Disc factorization in terms of lower-point building blocks. This framework provides a practical, constructive path to apply flat-space techniques—such as unitarity-based methods, BCFW-type constructs, and dispersion relations—to cosmological correlators and wavefunction coefficients, with natural extensions to spinning fields and more general spacetimes.

Abstract

Using cosmological dressing rules, we uplift flat-space unitarity cuts to discontinuity relations for dS/EAdS observables. In this representation, Cutkosky delta functions map directly to "Disc" operations in the exchanged energy variable. This provides a transparent diagram by diagram origin of cosmological cutting rules. We illustrate this with explicit examples at tree level and one loop for conformally coupled scalars.

Figures (2)

• Figure 1: Witten diagrams representing 4-point correlation functions. (a) Exchange via solid (+) propagator. (b) Exchange via a dashed ($-$) propagator.
• Figure 2: One-loop Witten diagram for four point function in $\phi^4$ theory. (a) (++) exchange (b) ($--$) exchange.