From the Wavefunction of the Universe to In-In-Correlators: A Perturbative Map to All Orders

Both the Wavefunction of the Universe and the Schwinger-Keldysh in-in formalism are central tools for analyzing primordial cosmological observables, such as equal-time correlation functions. While their conceptual equivalence is well established, a systematic and explicit map between their diagrammatic expansions has remained elusive. In this article, I construct such a map by analyzing the relation between the two frameworks at the diagrammatic level. I show that diagrams contributing to correlation functions in the Wavefunction of the Universe approach can be uniquely reorganized into Schwinger-Keldysh diagrams. This correspondence holds to all orders in perturbation theory, including arbitrary numbers of interaction vertices and loops.