A Reduction Algorithm for Cosmological Correlators: Cuts, Contractions, and Complexity

Abstract: Cosmological correlators are fundamental observables in an expanding universe and are highly non-trivial functions even at tree-level. In this work, we uncover novel structures in the space of such tree-level correlators that enable us to develop a new recursive algorithm for their explicit computation. We begin by formulating cosmological correlators as solutions to GKZ systems and develop a general strategy to construct additional differential operators, called reduction operators, when a GKZ system is reducible. Applying this framework, we determine all relevant reduction operators, and show that they can be used to build up the space of functions needed to represent the correlators. Beyond relating different integrals, these operators also yield a large number of algebraic relations, including cut and contraction relations between diagrams. This implies a significant reduction in the number of functions needed to represent each tree-level cosmological correlator. We present first steps to quantify the complexity of our reduction algorithm by using the Pfaffian framework. While we focus on tree-level cosmological correlators, our approach provides a blueprint for other perturbative settings.