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Cosmological scattering equations at tree-level and one-loop

Gomez, Humberto; Jusinskas, Renann Lipinski; Lipstein, Arthur

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Authors

Humberto Gomez

Renann Lipinski Jusinskas



Abstract

We recently proposed a formula for tree-level n-point correlators of massive phi^4 theory in de Sitter momentum space which consists of an integral over n punctures on the Riemann sphere and differential operators in the future boundary dubbed the cosmological scattering equations. This formula was explicitly checked up to six points via a map to Witten diagrams using the global residue theorem. In this work we provide further details of these calculations and present an alternative formulation based on a double cover of the Riemann sphere. This framework can be used to derive simple graphical rules for evaluating the integrals more efficiently. Using these rules, we check the validity of our formula up to eight points and sketch the derivation of n-point correlators. Finally, we propose a similar formula for 1-loop n-point correlators in terms of an integral over (n+2) punctures on the Riemann sphere, which we verify at four points. The 1-loop formula holds for small masses in de Sitter space and arbitrary masses satisfying the Breitenlohner-Freedman bound after Wick-rotating to Anti-de Sitter space.

Citation

Gomez, H., Jusinskas, R. L., & Lipstein, A. (2022). Cosmological scattering equations at tree-level and one-loop. Journal of High Energy Physics, 2022(7), Article 4. https://doi.org/10.1007/jhep07%282022%29004

Journal Article Type Article
Acceptance Date May 31, 2022
Online Publication Date Jul 1, 2022
Publication Date 2022
Deposit Date Jul 3, 2022
Publicly Available Date Jul 4, 2022
Journal Journal of High Energy Physics
Print ISSN 1126-6708
Publisher Scuola Internazionale Superiore di Studi Avanzati (SISSA)
Peer Reviewed Peer Reviewed
Volume 2022
Issue 7
Article Number 4
DOI https://doi.org/10.1007/jhep07%282022%29004
Related Public URLs https://arxiv.org/abs/2112.12695

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.





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