Andrzej Pokraka (U. of Amsterdam)

A graphical coaction for FRW cosmological correlators

Abstract: FRW cosmological correlators are expressed in terms of linear combinations of twisted integrals associated to special hyperplane arrangements. These twisted integrals evaluate to hypergeometric functions that depend on a collection of (generic) variables parameterizing the underlying QFT and FRW spacetime. When treated as small parameters these hypergeometric functions have Laurent expansions with multiple-polylogarithms (MPLs) as coefficients. Consequently, the coaction on MPLs provides strong constraints on the Laurent expansion of these hypergeometric functions.

In this talk, I will argue that certain decorated graphs describe the geometry of cosmological hyperplane arrangements. Using ideas from positive geometry, I will build a canonical basis of (co)homology from these decorated graphs. Then, using the framework of partially twisted (co)homology and intersection theory, I will derive a graphical coaction for the hypergeometric functions themselves that is compatible with the coaction on MPLs. The final form of this cosmological coaction parallels that of the diagrammatic coaction for Feynman integrals.