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.

A de Sitter S-matrix from amputated cosmological correlators

Leite Pimentel, Guilherme
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.
2024
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
de Sitter space; Cosmological models; Effective Field Theories
   MUR Programma per giovani ricercatori R.L. Montalcini, bando 2019: Il Bootstrap Cosmologico -- Scoprire la semplicità nelle condizioni iniziali dell'universo. [FFO 2019]
   MUR_DM-1152-21
   Ministero della pubblica istruzione, dell'università e della ricerca

   Assegnazione individuale per il supporto all’avvio della ricerca dei nuovi professori nel loro primo anno di attività presso la Scuola.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/146043
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