A Mellin Approach to Scattering in de Sitter

Boundary correlators in (anti)-de Sitter space-times are notoriously difficult beasts to tame. In AdS, where such observables are equivalent to CFT correlation functions, recent years have seen significant progress in our understanding of their structure owing to the development of numerous systematic techniques, many of which have drawn inspiration from the successes and the strengths of the scattering amplitudes programme in flat space. In dS however, the problem is more complicated owing to the time-dependence of the background and it is unclear how consistent time evolution is encoded in spatial correlations on the boundary. This makes application of our hard-earned wisdom from flat and AdS spaces far from straightforward. In this talk we explain how boundary correlators in AdS and dS can be placed on an equal footing by adopting a Mellin-Barnes representation in momentum space, providing a framework in which techniques and results available in AdS can be generalised to de Sitter.  This connection allows us to systematically derive expressions for boundary correlators in de Sitter involving fields with and without spin. Throughout we shall keep in mind applications to the classification of possible non-Gaussianities in cosmological correlation functions, of both scalar and tensor fluctuations.