A Graphical Coaction for FRW Wavefunction Coefficients

TL;DR

This paper introduces a graphical coaction framework for analyzing the wavefunction of the universe in conformally coupled scalar theories within FRW cosmologies, revealing its analytic structure through Feynman graph minors.

Contribution

It extends the graphical coaction approach to all particle multiplicities and loop orders, connecting it to the wavefunction's differential equations and discontinuities.

Findings

Graphical coaction captures the wavefunction's analytic structure.

Reproduces the kinematic flow from weight-one contributions.

Easily extracts discontinuities of wavefunction coefficients.

Abstract

We show that the wavefunction of the universe in theories of conformally coupled scalars in power-law Friedmann-Robertson-Walker (FRW) cosmologies satisfies a graphical coaction, by means of which we can understand its complete analytic structure in terms of the acyclic minors of Feynman graphs. Our construction extends to all particle multiplicities and any loop order, and if we isolate certain weight-one contributions, it reproduces the ``kinematic flow'' that encodes the differential equation of the wavefunction coefficients. Similarly, any discontinuity of the wavefunction coefficient is easily extracted from the coaction.