There and Back Again: Mapping and Factorising Cosmological Observables

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.