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We derive a cutting rule for equal-time in-in correlators, including cosmological correlators based on Keldysh r/a basis, which decomposes diagrams into fully retarded functions and cut-propagators consisting of Wightman functions. Our derivation relies only on basic assumptions such as unitarity, locality, and the causal structure of the in-in formalism. We apply the cutting rule to simplify the extraction of non-local cosmological collider signals, and prove the absence of one-loop scale-invariant corrections from enhanced small-scale perturbations to superhorizon curvature and tensor perturbations.
Junwu Huang, Pedro Bittar