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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Acknowledgments
It is a pleasure to thank the participants of the workshop “Correlators in Cortona” (Sep 2023) for many useful discussions, as well as Dionysios Anninos, Santiago Agüí Salcedo, Tarek Anous, Nima Arkani-Hamed, Daniel Baumann, Paolo Benincasa, Carlos Duaso Pueyo, Austin Joyce, Hayden Lee, Juan Maldacena, Enrico Pajer, Sasha Polyakov, and Dong-Gang Wang for useful discussions during this work. SM is supported by a UKRI Stephen Hawking Fellowship (EP/T017481/1). GLP is supported by Scuola Normale, by a Rita-Levi Montalcini fellowship from the Italian Ministry of Universities and Research (MUR), and by INFN (IS GSS-Pi).
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Melville, S., Pimentel, G.L. A de Sitter S-matrix from amputated cosmological correlators. J. High Energ. Phys. 2024, 211 (2024). https://doi.org/10.1007/JHEP08(2024)211
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DOI: https://doi.org/10.1007/JHEP08(2024)211