A Cosmological BCFW Bridge and Its Canonical Geometry

Abstract

We build a BCFW-like recursion for cosmological correlators using the orthogonal Grassmannian. The key step is a bridge deformation that leaves all the Grassmannian constraints intact. The recursion relations are purely algebraic and avoid any spectral or radial integrals that usually appear in curved space. We obtain the gluon 4-point correlator using this bridge, producing two factorization poles, a total energy singularity coming from the three point building block, and a shifted energy singularity that emerges only after adding the two channels using recursion. We then show that the helicity stripped four-gluon correlator has the canonical form of a rectangle, where its boundaries represent various poles. We also describe the geometry of the gluon correlator in the Pfaffians as the natural coordinates in the Grassmannian. Using multiple deformation bridges, we also obtain the graviton four point correlator and observe a double-copy like relation at the level of the four point function, away from the physical cuts for each channel. We also extended the BCFW bridge formalism to the supersymmetric Grassmannian.