A de Sitter S-matrix from amputated cosmological correlators
arxiv(2024)
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.
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