Regulating Loops in dS

Abstract

Perturbative QFT calculations in de Sitter are plagued by a variety of divergences. One particular kind, the secular growth terms, cause the naive perturbation expansion to break down at late times. Such contributions often arise from loop integrals, which are notoriously hard to compute in dS. We discuss an approach to evaluate such loop integrals, for a scalar field theory in a fixed de Sitter background. Our method is based on the Mellin-Barnes representation of correlation functions, which enables us to regulate divergences for scalars of any mass while preserving the symmetries of dS. The resulting expressions have a similar structure as a standard dimreg answer in flat space QFT. These features of the regulator are illustrated with two examples. Along the way, we illuminate the physical origin of these divergences and their interpretation within the framework of the dynamical renormalization group. Our calculations naturally reveal additional infrared divergences for massless scalar fields in de Sitter, that are not present in the massive case. Such loop corrections can be incorporated as systematic improvements to the Stochastic Inflation framework, allowing for a more precise description of the IR dynamics of massless fields in de Sitter.