A Simplified Born Rule for Cosmological Correlators
Abstract
Cosmological correlators are natural observables of the primordial universe and are related to wavefunction coefficients by the Born rule. For equal-time in-in correlators in flat spacetime, we prove that all double-boundary poles cancel for arbitrary graphs, including in theories with local derivative interactions. These cancellations occur before integration over spatial loop momenta and yield a simplified Born rule in terms of what we call embedded wavefunction coefficients. The resulting expansion reveals which physical poles can occur together while keeping the interaction dependence explicit. For conformally coupled Tr(ϕ3) theory in flat spacetime, the simplified Born rule takes the form of a uniformly weighted forest-cut expansion. From its pole combinatorics, we construct what we call the Born polytope, whose canonical function reproduces the normalized correlator for arbitrary graphs after matching its facet supports to the physical energies. The same geometry also yields a stringy formula for correlators.
Related
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BibTeX
@misc{zhu2026simplified,
title = {{A Simplified Born Rule for Cosmological Correlators}},
author = {Fan Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40412},
eprint = {2610.40412},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40412},
}
RIS
TY - UNPB
TI - A Simplified Born Rule for Cosmological Correlators
AU - Fan Zhu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40412
UR - https://arxiv.org/abs/2610.40412
AB - Cosmological correlators are natural observables of the primordial universe and are related to wavefunction coefficients by the Born rule. For equal-time in-in correlators in flat spacetime, we prove that all double-boundary poles cancel for arbitrary graphs, including in theories with local derivative interactions. These cancellations occur before integration over spatial loop momenta and yield a simplified Born rule in terms of what we call embedded wavefunction coefficients. The resulting expansion reveals which physical poles can occur together while keeping the interaction dependence explicit. For conformally coupled Tr(ϕ^3) theory in flat spacetime, the simplified Born rule takes the form of a uniformly weighted forest-cut expansion. From its pole combinatorics, we construct what we call the Born polytope, whose canonical function reproduces the normalized correlator for arbitrary graphs after matching its facet supports to the physical energies. The same geometry also yields a stringy formula for correlators.
ER -