The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities
In flat space, symmetries and singularities can be used to fully determine the structure of 4-particle scattering amplitudes at tree level. In this talk, I will describe how a similar logic can be used to uniquely fix the structure of tree-level inflationary correlation functions with approximate conformal symmetry, without reference to a Lagrangian description. I will present analytic solutions for the inflationary 3- and 4-point functions of conformally-coupled/massless scalars with arbitrary spin exchange, and show how these objects are related to each other via simple differential operators. As a result, the most general 3- and 4-point functions arising from weakly broken conformal symmetry are completely characterized by two basis functions up to coupling constants. Moreover, these inflationary correlators “contain” flat-space scattering amplitudes via an analytic continuation, providing a nontrivial link between scattering in flat space and particle production in curved space.