Exact Color Kinematics Duality in the Cosmological Correlators

Abstract

In this paper, we study color kinematics duality and related double-copy and BCJ structures in the cosmological Grassmannian framework. The simplicity of these correlators in this framework makes it possible to test the double copy construction beyond flat space. We show that the four-point gluon correlator admits a representation whose kinematic numerators satisfy an algebraically exact Jacobi identity, $n_s$ + $n_t$ + $n_u$ = 0. Replacing color factors with kinematic numerators gives a graviton correlator that reproduces the correct factorization residues and flat-space limit, which matches with the BCFW result up to terms regular in all exchange channels. In addition, we construct a differential bi-adjoint scalar matrix whose null vector gives rise to a differential BCJ relation among color-ordered gluon correlators. We further explore an s-copy construction for general integer-spin correlators and show that for odd spin the corresponding numerators satisfy a Jacobi identity. Finally, we develop a differential representation for scalar four-point correlators with gluon exchange. These results establish algebraic and differential aspects of graviton and gluon correlators in curved spacetime.

arXiv comment14 pages main text, no appendix. V2: References added, made changes to abstract and title