Schwinger-Keldysh Cosmological Cutting Rules

TL;DR

This paper develops and verifies unitarity-based cutting rules for cosmological correlators within the Schwinger-Keldysh formalism, revealing parallels with flat-space scattering amplitudes and addressing unique diagrammatic subtleties.

Contribution

It introduces a novel set of cutting rules directly at the level of cosmological observables, extending previous wavefunction-focused results to observable correlators.

Findings

Derived diagrammatic cutting rules for cosmological correlators.

Verified rules at tree level and with loop corrections.

Identified specific diagram combinations necessary for correlator discontinuities.

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.