Regulating Loops in dS

Perturbative QFT calculations in de Sitter space are riddled with contributions that diverge over time. These contributions often arise from loop integrals, which are notoriously hard to compute in de Sitter. 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 allow us to regulate divergences for scalars of any mass while preserving the de Sitter symmetries. The resulting expressions have a similar structure as a standard answer from dimensional regularization in flat space QFT. These features of the regulator are illustrated with two examples, worked out in detail. Along the way, we illuminate the physical origin of these divergences and their interpretation with the machinery of the dynamical renormalization group. Our approach regulates the IR divergences of massless and massive particles in the same way. For massless scalars, the loop corrections can be incorporated as systematic improvements to the Stochastic Inflation framework, allowing for a more precise description of the IR dynamics of such fields in de Sitter.