Cutting rule for in-in correlators and cosmological collider

TL;DR

This paper introduces a cutting rule for in-in correlators in cosmology, simplifying calculations and clarifying the origin of non-local signals by decomposing diagrams into retarded functions and cut-propagators.

Contribution

The authors derive a general cutting rule for in-in correlators based on the Keldysh r/a basis, applicable at any loop order and for arbitrary particle content.

Findings

Non-local cosmological signals originate solely from cut-propagators.

The cutting rule simplifies conformal time integrals by removing theta functions.

The derivation relies only on unitarity, locality, and causality, making it broadly applicable.

Abstract

We derive a cutting rule for equal-time in-in correlators including cosmological correlators based on Keldysh $r/a$ basis, which decomposes diagrams into fully retarded functions and cut-propagators consisting of Wightman functions. Our derivation relies only on basic assumptions such as unitarity, locality, and the causal structure of the in-in formalism, and therefore holds for theories with arbitrary particle contents and local interactions at any loop order. As an application, we show that non-local cosmological collider signals arise solely from cut-propagators under the assumption of microcausality. Since the cut-propagators do not contain (anti-)time-ordering theta functions, the conformal time integrals are factorized, simplifying practical calculations.