A de Sitter S-matrix from amputated cosmological correlators

TL;DR

This paper develops a framework for calculating the de Sitter S-matrix using off-shell correlators, simplifying computations and deriving explicit 3- and 4-particle scattering amplitudes relevant for cosmological collider signals.

Contribution

It introduces a novel off-shell correlator approach for de Sitter spacetime, providing compact expressions for scalar scattering amplitudes and a spectral decomposition for heavy field exchanges.

Findings

Derived compact 3- and 4-particle S-matrices at tree-level

Found the 3-particle and exchange 4-particle S-matrices are unique up to crossing

Introduced a spectral decomposition for heavy field exchange in cosmological collider signals

Abstract

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.