  We study the O(N) scalar field theory with quartic self-coupling in de Sitter
space. When the field is light in units of the expansion rate, perturbative
methods break down at very low momenta due to large infrared logarithmic terms.
Using the nonperturbative large-N limit, we compute the four-point vertex
function in the deep infrared regime. The resummation of an infinite series of
perturbative (bubble) diagrams leads to a modified power law which is analogous
to the generation of an anomalous dimension in critical phenomena. We discuss
in detail the role of high momentum (subhorizon) modes, including the issue of
renormalization, and show that they influence the dynamics of infrared
(superhorizon) modes only through a constant renormalization factor. This
provides an explicit example of effective decoupling between high and low
energy physics in an expanding space-time.
