Cosmological Scattering

I will outline different approaches to describing 'scattering' on cosmological spacetimes. Scattering - describing what will emerge from a system if a known state is thrown in - plays a foundational role in our understanding of quantum field theory on flat Minkowski spacetime. Fundamental physical properties (e.g.  causality) correspond to distinct mathematical features of the S-matrix and its phase shifts (e.g. analyticity), which have been used to derive many non-trivial constraints on the phenomenology of low-energy particle collisions. The motivation for developing an analogous machinery for curved spacetimes is to achieve the same dictionary between fundamental physical principles and concrete mathematical properties - which can ultimately be used to constrain our cosmological models. Recently, there have been some hints that causality continues to impose powerful (and practically useful) constraints on these non-trivial backgrounds, which I will describe.