Breakdown of Semiclassical Methods in de Sitter Space

TL;DR

The paper analyzes the breakdown of semiclassical methods for massless or very light scalar fields in de Sitter space due to infrared fluctuations. It develops a power-counting framework for IR contributions to in-in correlators in a $\lambda\phi^4$ theory and draws an analogy to finite-temperature field theory, identifying per-loop IR enhancements that threaten perturbative control. A key result is that loop corrections become unsuppressed when $m^2$ approaches $\sqrt{\lambda}\,(H/(2\pi))^2$, with resummations that introduce a thermal-like mass offering partial relief but not a complete cure in general; the breakdown is encoded in IR-divergent or mass-enhanced terms that scale as $\left(\dfrac{\lambda H^4}{4\pi^2 m_0^4}\right)^L$. The findings have potential implications for inflationary cosmology, suggesting that mean-field-based calculations in the IR may be unreliable and motivating nonperturbative approaches, while noting that pure gravity and some Goldstone sectors may evade the same breakdown under certain conditions.

Abstract

Massless interacting scalar fields in de Sitter space have long been known to experience large fluctuations over length scales larger than Hubble distances. A similar situation arises in condensed matter physics in the vicinity of a critical point, and in this better-understood situation these large fluctuations indicate the failure in this regime of mean-field methods. We argue that for non-Goldstone scalars in de Sitter space, these fluctuations can also be interpreted as signaling the complete breakdown of the semi-classical methods widely used throughout cosmology. By power-counting the infrared properties of Feynman graphs in de Sitter space we find that for a massive scalar interacting through a λφ^4$ interaction, control over the loop approximation is lost for masses smaller than m \simeq \sqrt λH/2π, where H is the Hubble scale. We briefly discuss some potential implications for inflationary cosmology.