Cosmological scattering equations at tree-level and one-loop

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

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
• Electronic ISSN: 1029-8479
• 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
• Public URL: https://durham-repository.worktribe.com/output/1200497
• Related Public URLs: https://arxiv.org/abs/2112.12695