There and Back Again: Mapping and Factorising Cosmological Observables

TL;DR

This paper introduces a duality between cosmological correlators and wavefunction coefficients, revealing a $ ext{Z}_4$ symmetry, and derives new factorisation and cutting rules for correlators that are physically testable.

Contribution

It establishes a duality valid to all loop orders and derives the first physically testable correlator cutting rules using this duality.

Findings

Derived a correlator-to-correlator factorisation formula.

Established a $ ext{Z}_4$ symmetry duality between correlators and wavefunction coefficients.

Formulated testable cutting rules for cosmological correlators.

Abstract

Cosmological correlators encode invaluable information about the wavefunction of the primordial universe. In this letter we present a duality between correlators and wavefunction coefficients that is valid to all orders in the loop expansion and manifests itself as a $\mathbb{Z}_4$ symmetry. To demonstrate the power of the duality, we derive a correlator-to-correlator factorisation (CCF) formula for the parity-odd part of cosmological correlators that relates $n$-point observables to lower-point ones via a series of diagrammatic cuts. These relations serve as the first example of physically testable cutting rules as they involve observables defined for arbitrary physical kinematics. We further show how the duality allows us to translate the cosmological optical theorem for wavefunction coefficients into statements about cosmological correlators.