Propagator positivity bounds for cosmological correlators

Using unitarity and causality, we derive an infinite tower of two-sided positivity bounds on the effective field theory coefficients which describe the propagation of heavy fields on de Sitter spacetime. We design this effective field theory (EFT) to describe propagators with the in-in boundary conditions that are relevant for cosmological correlators. Our positivity bounds therefore identify EFT correlators that can never emerge from a consistent underlying model of inflation. This implies nontrivial constraints on primordial non-Gaussianity; for instance the cosmological collider oscillations in the squeezed bispectrum from the exchange of a heavy scalar are tied to the shape of its EFT background.