All Tree-Level Massive Cosmological Correlators via Spectral Gluing

Massive cosmological correlators exhibit a rich hypergeometric structure already at tree level, reflecting the distorted propagation of particles in de Sitter spacetime. In this paper, we reveal that this apparent complexity conceals a remarkably simple underlying mathematical structure. Using the spectral representation, we compute arbitrary tree-level correlators of scalar fields with generic masses and show that they are constructed from fundamental building blocks belonging to the family of Lauricella generalised hypergeometric functions, glued together by spectral integrals. We develop a spectral gluing algorithm that evaluates these integrals through elementary graph combinatorics, yielding explicit series representations that resum the dependence on internal energies away from soft limits. This algorithm naturally generates solutions to the differential equations satisfied by massive correlators as expansions in the corresponding eigenfunctions. Acting with a set of graph annihilators, we uncover a new class of magical identities among generalised hypergeometric functions, revealing an unexpected simplification: once the dynamical propagators are stripped away, the remaining hypergeometric kinematic dependence collapses to rational functions. Our results expose a hidden simplicity in the rigid hypergeometric analytic structure dictated by graph combinatorics, and hint at an intrinsic geometric principle from which properties of massive correlators naturally emerge.