The Cosmological Grassmannian

TL;DR

This paper introduces the orthogonal Grassmannian as a new geometric framework for simplifying and understanding correlators of massless spinning fields in de Sitter space, revealing deep connections to scattering amplitudes.

Contribution

The paper develops the orthogonal Grassmannian formalism for de Sitter correlators, unifies kinematic constraints, and demonstrates its effectiveness in bootstrapping four-point functions including Yang-Mills theory.

Findings

Three-point functions are fixed by little group covariance.

Four-point functions can be bootstrapped using unitarity and factorization.

The Grassmannian formalism reveals a close connection to scattering amplitudes.

Abstract

We introduce the orthogonal Grassmannian as a novel kinematic space for describing correlators of massless spinning fields in de Sitter space. By automatically encoding the constraints of conformal symmetry and current conservation, the formalism drastically simplifies these correlators. We show that three-point functions are fixed by little group covariance and take the same form as the corresponding Schwinger-parameterized correlators in twistor space. The power of the Grassmannian approach is especially evident for four-point functions, which require dynamical input beyond kinematics. We demonstrate that unitarity enforces the same factorization properties as for scattering amplitudes and use these to bootstrap the four-point functions in several non-trivial examples, including Yang-Mills theory. We find expressions that are astonishingly simple and reveal a close connection to the corresponding scattering amplitudes. Our results suggest that the Grassmannian provides the natural language for spinning correlators in de Sitter space and illuminates their geometric origin.