Cosmological Collider in the Grassmannian

TL;DR

This paper derives a closed-form expression for four-point wavefunction coefficients in cosmological collider physics using Grassmannian geometry, simplifying calculations in the de Sitter limit.

Contribution

It introduces a Grassmannian-based method to compute cosmological correlators in closed form, incorporating spin and mass effects more simply than traditional momentum-space approaches.

Findings

Derived a hypergeometric function representation of the correlator.

Expressed spin dependence as Legendre polynomial factors.

Demonstrated the Grassmannian approach simplifies cosmological calculations.

Abstract

We revisit the computation of four-point wavefunction coefficients for external conformally coupled scalars exchanging a particle of general mass and spin. Much of the phenomenology of cosmological collider physics in the near-de Sitter limit follows from this function. Computing it in detail is a central challenge in the cosmological bootstrap. Using the cosmological Grassmannian, we write this correlator in closed form using hypergeometric functions and Legendre polynomials. We achieve this by writing the standard bootstrap differential equation using the Pl\"ucker coordinates of the Grassmannian, and using the basis of Mandelstam invariants. The correlator 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 by further matching to kinematic limits of the momentum-space wavefunction. 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.