Cosmology meets cohomology

The recent study of FRW correlators has revealed fascinating connections between positive geometries and modern on-shell methods as well as exhibiting novel mathematical structures. In particular, FRW correlators take the form of (degenerate) generalized Euler integrals. I will formulate the associated twisted cohomology governing these integrals then introduce the intersection pairing (an inner product on the space of FRW integrals) and the corresponding dual relative twisted cohomology. Then, I will advocate for the advantages of relative twisted cohomology; specifically how it manifests the unitarity structure of these correlators. Using this framework, I will explain how to predict the basis size of these integrals and describe several algorithms to compute their differential equations.