Cosmological Collider in the Grassmannian

Abstract

We revisit the computation of four-point wavefunction coefficients and correlators for external conformally coupled scalars exchanging a particle of generic mass and spin. Much of the phenomenology of cosmological collider physics in the near-de Sitter limit follows from these functions. Computing them in detail is a central challenge in the cosmological bootstrap. Using the cosmological Grassmannian, we write these objects in closed form using hypergeometric functions and Legendre polynomials. We achieve this by writing the standard bootstrap differential equation using the Plücker coordinates of the Grassmannian, and using the basis of Mandelstam invariants. The exchange in the s-channel can be written in terms of a hypergeometric function of the S Mandelstam, while the spin information appears as an overall Legendre polynomial factor that also depends on the other Mandelstams. We fix the boundary conditions by first demanding the absence of unphysical singularities, and, for correlators, by further matching to a kinematic limit in momentum space. Our formulae in Grassmannian space are much simpler than their counterparts in momentum space, demonstrating another useful application of the Grassmannian as a kinematic space for cosmology.