# A Mellin Space Approach to Cosmological Correlators

## TL;DR

This paper introduces a Mellin space framework for analyzing late-time cosmological correlators in de Sitter space, simplifying their structure and enabling a unified treatment of scalar interactions in arbitrary dimensions.

## Contribution

It develops a general Mellin-Barnes representation for cosmological correlators, providing explicit formulas for scalar contact and exchange diagrams in arbitrary dimensions.

## Key findings

- Correlators expressed as hypergeometric functions.
- Reduces to known results for specific dimensions and scalar types.
- Framework applicable to both de Sitter and anti-de Sitter spaces.

## Abstract

We propose a Mellin space approach to the evaluation of late-time momentum-space correlation functions of quantum fields in $\left(d+1\right)$-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 $\left(d+1\right)$-dimensional anti-de Sitter space (Witten diagrams).