Dynamical RG and Critical Phenomena in de Sitter Space

TL;DR

Seeks to understand time-dependent, secular divergences in perturbative QFT on de Sitter space. It shows these divergences originate from flat-space anomalous dimensions and can be resummed using the dynamical renormalization group, with the effective scaling controlled by Δ+γ(H). The authors develop a conformal perturbation theory framework and apply it to conformally coupled scalars in 4 and 4-ε, as well as Yukawa interactions, establishing a robust link between flat-space RG data and de Sitter late-time behavior. The results provide a unified picture of IR secular effects in de Sitter and offer a calculable route to their resummation, with implications for inflationary cosmology and the interpretation of IR divergences in curved spacetime.

Abstract

Perturbative quantum field theory in de Sitter space is known to give rise to a variety of contributions that diverge with time (secular terms). Despite significant progress, a complete understanding of the physical origin of these divergences remains an outstanding problem. In this paper, we will study the origin of secular divergences in de Sitter space for interacting theories that are near attractive conformal fixed points. We show that the secular divergences are determined by the anomalous dimensions of the same theory in flat space and can be re-summed using the dynamical renormalization group. This behavior is mandatory at the conformal fixed point but we show that it holds away from the fixed point as well. We analyze this problem in general using conformal perturbation theory and study conformally coupled scalar fields in four and $4-ε$ dimensions as examples.

Figures (1)

• Figure 1: The Feynman diagrams involved in the calculation of $\braket{\phi^2 \phi^2}$.