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

TL;DR

This paper demonstrates that infrared divergences in de Sitter spacetime can be managed with standard perturbative techniques, showing that loop corrections do not necessarily cause secular growth in correlation functions when proper regularization is applied.

Contribution

It shows that infrared divergences in de Sitter space can be regularized using dimensional regularization and counterterms, preventing secular growth from loop corrections.

Findings

Loop corrections can be handled without introducing secular growth.

Infrared divergences are eliminated with counterterms at each perturbation order.

Cutoffs and time-dependent Wilsonian coefficients are crucial for cutoff-independent observables.

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 $\varphi$ with self-interactions described by a potential $\mathcal{V}(\varphi)$, 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 $\mathcal{V}_{\rm eff}(\varphi)$, 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.