Andrzej Pokraka, "A Coaction for Cosmological Integrals"

Cosmological correlators, like scattering amplitudes, are built from integrals whose analytic structure can be organised by a coaction. Here, I will explain how this works for the wavefunction of the universe in theories of conformally coupled scalars in power-law Friedmann–Robertson–Walker (FRW) cosmologies. The wavefunction satisfies a graphical coaction, by means of which we can understand its complete analytic structure in terms of decorated (acyclic minors) of Feynman graphs. The construction extends to all particle multiplicities and any loop order. Isolating certain weight-one contributions reproduces the “kinematic flow” that encodes the differential equations of the wavefunction coefficients, and the (sequential) discontinuities can be extracted in the same way. Since both follow from the same enumeration of decorated Feynman graphs, the coaction reduces the determination of the differential equations and discontinuities of any wavefunction coefficient to a combinatorial problem.