Reconstructing cosmological correlators via dispersion: from cutting to dressing rules

TL;DR

This paper develops a method to reconstruct cosmological correlators in de Sitter space using dispersion formulas and cutting rules, connecting flat-space Feynman diagrams to cosmological observables and emphasizing unitarity principles.

Contribution

It introduces a systematic approach to reconstruct cosmological correlators from their discontinuities using dispersion relations and cutting rules, applicable to tree-level diagrams with multiple vertices.

Findings

Reconstruction of correlators from lower-point objects and discontinuities.

Application of cutting rules to multiple internal lines in diagrams.

Rediscovery of dressing rules linking flat-space diagrams to de Sitter correlators.

Abstract

In this work, we investigate how cosmological correlators can be reconstructed by applying the momentum-space dispersion formula to their discontinuities, treating them as functions of momentum variables associated with the corresponding de Sitter Witten diagrams. We focus on conformally coupled and massless polynomial scalar interactions (both IR-divergent and IR-convergent), and consider tree-level de Sitter Witten diagrams. We explicitly utilize the single-cut discontinuity relations, or cutting rules, involving the cosmological correlators recently constructed in arXiv:2512.20720. For diagrams with multiple interaction vertices, we apply the dispersion formula by cutting all internal lines in the diagram one by one, successively, thereby allowing us to reconstruct the full correlator using only lower-point contact-level objects and their discontinuity data, up to contact diagram ambiguities. We also rediscover how the cosmological correlators on the late-time slice of de Sitter space can be obtained from flat-space Feynman diagrams via a set of dressing rules. Our starting point, being the cutting rules for the cosmological correlators, also emphasizes how basic principles, such as unitarity for in-in correlators, can lead us to the dressing rules, which were previously derived in literature following a different method.