The Cosmological Grassmannian

TL;DR

This paper introduces the orthogonal Grassmannian $\mathrm{OGr}(n,2n)$ as a natural kinematic space for massless spinning correlators in de Sitter space, encoding conformal symmetry and current conservation to drastically simplify calculations. The authors formulate wavefunction coefficients as Grassmannian integrals $\psi_n(\Lambda)=\int dC\, \delta(C\cdot\Lambda)\, A_n(C)$, show that three-point functions are fixed by little-group covariance and relate them to Schwinger-parameterized twistor-space correlators, and bootstrap four-point functions using unitarity-based factorization with remarkably simple results. They present explicit Grassmannian representations for Yang–Mills four-point correlators and demonstrate how dispersion reconstructs the full momentum-space correlators from discontinuities, establishing a close connection to flat-space scattering amplitudes. The framework suggests a geometric origin for spinning cosmological correlators and offers a path toward unifying cosmological observables with scattering-amplitude structures, potentially extending to gravity and higher-point functions. Overall, the work provides a compact, on-shell-like language for spinning cosmological correlators with powerful bootstrap tools and transparent flat-space limits.

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.

Figures (3)

• Figure 1: Illustration of the different spaces used in this paper. Twistor space is related to momentum space by a half-Fourier transform and to the Grassmannian space by an ordinary Fourier transform. The integral transform in \ref{['equ:main-integral']} maps Grassmannian correlators directly to momentum space.
• Figure 2: Illustration of the possible poles in the $\tau$-plane and the choice of contour used in this section.
• Figure 3: In this appendix, we describe the flat-space limit in Grassmannian space, in which the correlator $A_n$ reduces to the amplitude ${\cal M}_n$. We further show that, in this limit, the Grassmannian integral produces the flat-space amplitude $M_n$. This is complementary to the treatment in the main text, where the Grassmannian integral gives the wavefunction coefficient $\psi_n$ and the flat-space limit, which leads to the amplitude $M_n$, is taken in momentum space.