  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.
