Cosmology meets cohomology

TL;DR

This paper explores the intersection of cosmology and cohomology, introducing methods to efficiently compute complex integrals in cosmological models using geometric and differential equation techniques.

Contribution

It develops a geometric framework using relative twisted cohomology and an algorithm to simplify the computation of FRW cosmological correlators.

Findings

Introduces a cohomological approach to cosmological integrals

Provides an algorithm for basis prediction and simplification

Enhances computational efficiency for FRW correlators

Abstract

The cosmological polytope and bootstrap programs have revealed interesting connections between positive geometries, modern on-shell methods and bootstrap principles studied in the amplitudes community with the wavefunction of the Universe in toy models of FRW cosmologies. To compute these FRW correlators, one often faces integrals that are too difficult to evaluate by direct integration. Borrowing from the Feynman integral community, the method of (canonical) differential equations provides an efficient alternative for evaluating these integrals. Moreover, we further develop our geometric understanding of these integrals by describing the associated \emph{relative} twisted cohomology. Leveraging recent progress in our understanding of relative twisted cohomology in the Feynman integral community, we give an algorithm to predict the basis size and simplify the computation of the differential equations satisfied by FRW correlators.