Regularizing infrared divergences in de Sitter spacetime: Loops, dimensional regularization, and cutoffs

Abstract

Correlation functions of light scalar fields in de Sitter spacetime, computed via standard perturbation theory, often exhibit secular growth characterized by time-dependent divergent terms in the form of powers of $\ln a(t)$, where $a(t)$ is the scale factor describing cosmic expansion. It is widely believed that loop corrections further enhance this secular growth. We argue that this is not necessarily the case: Loop corrections can be systematically handled using standard perturbative techniques, such as dimensional regularization, without introducing new $\ln a(t)$ terms. We focus on a canonical massless scalar field $φ$ with self-interactions described by a potential $\mathcal{V}(φ)$, and analyze correlation functions represented by diagrams with a single vertex and an arbitrary number of loops. In this framework, infrared divergences can be systematically eliminated with counterterms at each order in perturbation theory, leading to loop-corrected correlation functions that are indistinguishable from their tree-level forms, with no secular growth from loops. Furthermore, adopting a Wilsonian perspective, we explore the role of cutoffs in computing loop corrections within effective field theory and identify the effective potential $\mathcal{V}_{\rm eff}(φ)$, which guarantees cutoff-independent observables. We conclude that when infrared comoving cutoffs are used to regularize loop integrals, time-dependent Wilsonian coefficients are necessary to maintain cutoff-free correlation functions. Neglecting this time dependence results in secular growth from loops.