Cosmological Correlator Discontinuities from Scattering Amplitudes

Abstract: Recent theoretical work has revealed that basic observables of quantum field theory in de Sitter space, known as in-in or cosmological correlators, exhibit surprisingly simple mathematical structure reminiscent of scattering amplitudes in flat space. For many theories, this simplicity can be made manifest using a set of ``cosmological dressing rules'' which uplift flat-space Feynman diagrams to in-in correlators in de Sitter space by attaching auxiliary propagators to the interaction vertices. In this paper, we show that discontinuities of cosmological correlators with respect to internal energy variables can be obtained by applying auxiliary propagators to unitarity cuts of flat space Feynman diagrams. Moreover, discontinuities with respect to external energy variables can be obtained by cutting auxiliary propagators attached to Feynman diagrams. This observation in turn implies highly non-trivial constraints on cosmological correlators in the form of simple sum rules. We illustrate these ideas in a number of examples at tree-level and 1-loop for conformally coupled scalar theories, although they hold more generally. Finally, we show how to reconstruct cosmological correlators from their discontinuities using dispersion relations, providing a powerful new approach to computing cosmological observables by systematically reconstructing them from data uplifted from flat space.