The study of interacting quantum fields in de Sitter geometry reveals
peculiarities that are of conceptual and phenomenological interest. In
this geometry, the exponential expansion of the metric produces an
effective growth in the self-interaction of light fields, breaking down
the standard perturbative expansion. Furthermore, in the massless limit
the free propagators do not respect the symmetries of the classical
theory, and neither do they decay at large distances.

One way to avoid the problems of the standard perturbative calculations
is to go to Euclidean de Sitter space, where the zero mode responsible
for IR divergences can be treated exactly, giving an effective coupling
sqrt{lambda} for the perturbative corrections coming from the
nonzero modes. The Lorentzian counterpart is then obtained by analytical
continuation. However, we point out that a further partial resummation
of the leading secular terms (which necessarily involves nonzero modes)
is required to obtain a decay of the two-point functions at large
distances for massless fields. We implement this resummation along with
a systematic double expansion in sqrt{lambda} and in 1/N in the
O(N) model. These results improve on those known in the leading
infrared approximation obtained directly in Lorentzian de Sitter
spacetime, while reducing to them in the appropriate limits.