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 $\textit{simplified Born rule}$ 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 $\operatorname{Tr}(ϕ^3)$ 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 $\textit{Born polytope}$, 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.