Regulating loops in de Sitter spacetime

Abstract

Perturbative quantum field theory (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 loop integrals that contribute to equal-time correlators of a scalar field theory in a fixed de Sitter background. Our method is based on the Mellin-Barnes representation of correlation functions, which allows us to regulate loop divergences by adjusting the masses of the fields, or by gently deforming the underlying de Sitter spacetime. 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.

arXiv comment38 pages, 10 figures. v2: Added closed form expression for anomalous dimension, and updated its plot. v3: Final version that was published in Physical Review D

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Cited by in corpus (5)

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• Towards Systematic Evaluation of de Sitter Correlators via Generalized Integration-By-Parts Relations
• Multivariate hypergeometric solutions of cosmological (dS) correlators by $\text{d}\log$-form differential equations
• The Asymptotic Structure of Cosmological Integrals
• Cosmological Infrared Subtractions & Infrared-Safe Computables