Notes on Diagrammatic Coaction for Cosmological Wavefunction Coefficients: A Two-Site Prelude

TL;DR

This paper explores the coaction structure of cosmological wavefunction coefficients using a two-site diagrammatic approach, revealing how coaction decomposes integrals into subtopologies with clear physical interpretations.

Contribution

It introduces a diagrammatic interpretation of coaction on cosmological wavefunction coefficients, linking subtopologies to time-ordered integrals and analytic structure.

Findings

Coaction decomposes wavefunction integrals into subtopologies.

Diagrammatic interpretation clarifies the analytic structure.

Potential applicability to more complex cosmological diagrams.

Abstract

We study the coaction of cosmological wavefunction coefficients of conformally coupled scalars in FRW background of a two-site example, which turns out to have an elegant diagrammatic interpretation. We show how the coaction acts on the twisted integrals for wavefunction coefficients, decomposing them into contributions associated with subtopologies and cuts, with the subtopologies admitting an interpretation as time-ordered integrals. This provides a clear interpretation of their analytic structure and suggests a broader applicability to more general cosmological diagrams.