Shibam Das | Searcharxiv

arXiv2026

Reconstructing cosmological correlators via dispersion: from cutting to dressing rules

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.

hep-th↗

arXiv2025

A single-cut discontinuity for cosmological correlators from unitarity and analyticity

We derive discontinuity relations, also known as cutting rules, and explore the analytic properties of cosmological correlators, fundamental observables of the primordial universe. Our emphasis is on how these relations arise from unitarity and hermitian analyticity in interacting quantum field theories on de Sitter space-time. Instead of analyzing wave-function coefficients, we apply these relations directly to cosmological correlators. By studying conformally coupled and massless scalar fields with $\phi^n$ self-interactions, we demonstrate that the discontinuity of a cosmological correlator can be expressed as a sum of products of lower-point discontinuities, stemming from a single-cut of one internal line in the corresponding tree-level exchange Witten diagram. Notably, beyond lower-point correlators, the decomposition of the discontinuities of cosmological correlators includes contributions from auxiliary elements that consist of both the real and imaginary parts of the lower-point wave-function coefficients, which have not been reported in the existing literature. Interestingly, depending on whether $n$ is even or odd in a $\phi^n$ interaction, these different lower-point discontinuities contribute as the leading or sub-leading piece in the late-time limit to the discontinuity relations. Additionally, our single-cut discontinuity relation leads to a decomposition rule for the residue of the cosmological correlators at partial energy singularities, incorporating contributions from these auxiliary objects. Through explicit calculations in several models, we confirm that our discontinuity relations are consistent with results from the in-in formalism. While primarily developed using tree-level exchanges with polynomial interactions, we also demonstrate that our framework can be extended to include loop corrections and cases with derivative interactions.

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