A Mellin space approach to cosmological correlators

TLDR: In this article, the Mellin-Barnes representation is used for the evaluation of late-time momentum-space correlation functions of quantum fields in (d + 1)-dimensional de Sitter space.

Abstract: We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in (d + 1)-dimensional de Sitter space. The Mellin-Barnes representation makes manifest the analytic structure of late-time correlators and, more generally, provides a convenient general d framework for the study of conformal correlators in momentum space. In this work we focus on tree-level correlation functions of general scalars as a prototype, including n-point contact diagrams and 4-point exchanges. For generic scalars, both the contact and exchange diagrams are given by (generalised) Hypergeometric functions, which reduce to existing expressions available in the literature for d = 3 and external scalars which are either simultaneously conformally coupled or massless. This approach can also be used for the perturbative bulk evaluation of momentum space boundary correlators in (d + 1)-dimensional anti-de Sitter space (Witten diagrams).