Schwinger-Keldysh Cosmological Cutting Rules
Francisco Colipí-Marchant, Gabriel Marin, Gonzalo A. Palma, Francisco Rojas
TL;DR
The paper develops unitarity-based cutting rules for cosmological correlators computed in the Schwinger-Keldysh formalism, showing that discontinuities of observables factorise into products of lower-point correlators, much like flat-space Cutkosky rules. A key innovation is the introduction of barred correlators, which encode the necessary real/imaginary combinations to express discontinuities in terms of lower-point data and to organize higher-topology cuts. The authors derive explicit tree-level results for an $s$-channel four-point diagram, extend the framework to general tree-level topologies with derivative couplings, and formulate a comprehensive cutting recipe that extends to one-loop diagrams. The approach provides a recursive, bootstrap-friendly path to compute higher-order cosmological correlators from basic building blocks, with potential links to the $r/a$ (Keldysh) basis and broader unitarity considerations in curved spacetimes.
Abstract
In this work, we study the realisation of unitarity-based cutting rules for primordial cosmological correlators computed within the Schwinger-Keldysh path integral formalism. While cutting rules have been previously derived for wavefunction coefficients, here we examine them directly at the level of cosmological observables expressed diagrammatically. The resulting rules closely resemble those familiar from flat-space scattering amplitudes, but with an additional subtlety: in order to express the discontinuity of a correlator as the product of lower-order correlators, one must introduce a specific combinations of diagrams which do not appear in the computation of observables themselves. We explicitly verify these rules for several classes of correlators, both at tree level and with loop corrections, arising from theories involving different types of interactions.