A de Sitter S-matrix from amputated cosmological correlators

A bstract Extending scattering to states with unphysical mass values (particles “off their mass shell”) has been instrumental in developing modern amplitude technology for Minkowski spacetime. Here, we study the off-shell correlators which underpin the recently proposed S -matrix for scattering on de Sitter spacetime. By labelling each particle with both a spatial momentum and an independent “energy” variable (the de Sitter analogue of a 4-momentum), we find that the practical computation of these correlators is greatly simplified. This allows us to derive compact expressions for all 3- and 4-particle S -matrices at tree-level for scalar fields coupled through any derivative interactions. As on Minkowski, we find that the 3-particle and exchange part of the 4-particle S -matrices are unique (up to crossing). The remaining contact part of the 4-particle S -matrix is an analytic function of just two differential operators, which become the usual Mandelstam variables in the Minkowski limit. Finally, we introduce a spectral decomposition for the tree-level exchange of a heavy field responsible for a cosmological collider signal. Once projected onto physical mass eigenstates, these S -matrix elements encode the statistical properties of the early inflationary perturbations.