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.

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- Théorie