Breakdown of Semiclassical Methods in de Sitter Space

TL;DR

This paper demonstrates that semiclassical methods in de Sitter space break down for certain scalar fields due to large fluctuations, especially for small masses, impacting inflationary cosmology models.

Contribution

It identifies the mass threshold below which semiclassical approximations become invalid for scalar fields in de Sitter space, revealing a fundamental limitation of current cosmological methods.

Findings

Semiclassical methods fail for scalar masses below ~√λ H/2π.

Large fluctuations indicate breakdown of mean-field approximations.

Implications for inflationary cosmology models are discussed.

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 \lambda \phi^4$ interaction, control over the loop approximation is lost for masses smaller than m \simeq \sqrt \lambda H/2\pi, where H is the Hubble scale. We briefly discuss some potential implications for inflationary cosmology.