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

TL;DR

This paper establishes a systematic, all-orders diagrammatic correspondence between the Wavefunction of the Universe and the Schwinger-Keldysh in-in formalism, enhancing understanding of cosmological correlators.

Contribution

It provides the first explicit, perturbative map between the diagrammatic expansions of the Wavefunction of the Universe and the in-in formalism, valid to all orders.

Findings

Diagrams in the Wavefunction approach can be uniquely reorganized into Schwinger-Keldysh diagrams.

The correspondence between the two formalisms holds at all perturbative orders, including loops.

This mapping clarifies the conceptual and computational relationship between the two frameworks.

Abstract

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.