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The cosmological tree theorem

Published version
Peer-reviewed

Repository DOI


Change log

Authors

Salcedo, Santiago Agüí 
Melville, Scott 

Abstract

jats:titleAjats:scbstract</jats:sc> </jats:title>jats:pA number of diagrammatic “cutting rules” have recently been developed for the wavefunction of the Universe which determines cosmological correlation functions. These leverage perturbative unitarity to relate particular “discontinuities” in Feynman-Witten diagrams (with cosmological boundary conditions) to simpler diagrams, in much the same way that the Cutkosky rules relate different scattering amplitudes. In this work, we make use of a further causality condition to derive new cutting rules for Feynman-Witten diagrams on any time-dependent spacetime background. These lead to the cosmological analogue of Feynman’s tree theorem for amplitudes, which can be used to systematically expand any loop diagram in terms of (momentum integrals of) tree-level diagrams. As an application of these new rules, we show that certain singularities in the wavefunction cannot appear in equal-time correlators due to a cancellation between “real” and “virtual” contributions that closely parallels the KLN theorem. Finally, when combined with the Bunch-Davies condition that certain unphysical singularities are absent, these cutting rules completely determine any tree-level exchange diagram in terms of simpler contact diagrams. Altogether, these results remove the need to ever perform nested time integrals when computing cosmological correlators.</jats:p>

Description

Acknowledgements: We thank Harry Goodhew, Mang Hei Gordon Lee, Prahar Mitra, Enrico Pajer and David Stefanyszyn for useful discussions. S.M. is supported by a UKRI Stephen Hawking Fellowship (EP/T017481/1). S.A.S. is supported by a Harding Distinguished Postgraduate Scholarship. This work has been partially supported by STFC consolidated grant ST/T000694/1. Note added. In the final stages of preparing this manuscript, [115] appeared on the arXiv, which discusses cutting rules from a different (polytope) perspective. It would be interesting to investigate how the causality conditions and loop-level cutting rules presented here could be recovered from the optical polytope of [115].

Keywords

4902 Mathematical Physics, 5107 Particle and High Energy Physics, 49 Mathematical Sciences, 51 Physical Sciences

Journal Title

Journal of High Energy Physics

Conference Name

Journal ISSN

1126-6708
1029-8479

Volume Title

2023

Publisher

Springer Science and Business Media LLC