Cosmological Correlator Discontinuities from Scattering Amplitudes

TL;DR

This work shows that cosmological correlators in $dS_4$ exhibit a structure that allows their discontinuities to be directly derived from flat-space scattering amplitudes via cosmological dressing rules. Internal-energy discontinuities $y^2$ are obtained by dressing unitarity cuts of flat-space diagrams, while external-energy discontinuities $x^2$ come from cutting auxiliary propagators attached to flat-space diagrams. These insights lead to simple sum rules and a dispersion-relations framework to reconstruct correlators from their discontinuities, providing a practical algorithm for computing cosmological observables from flat-space data. The authors illustrate the method with tree-level and one-loop examples for conformally coupled scalars, establishing a path toward bootstrapping cosmological correlators and linking de Sitter physics to flat-space 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.

Figures (1)

• Figure 1: The contour integral corresponding to Eq. \ref{['dispersive2']}. Note that, for two-site graphs, the integrand in Eq. \ref{['dispersive1.5']} is analytic in the $z$-plane except for branch cuts and/or poles corresponding to the folded and partial energy singularities, in addition to two simple poles at $z=\pm \sqrt{y^2}$.