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We consider an $O(N)$ scalar field model with quartic interaction in$d$-dimensional Euclidean de Sitter space. In order to avoid the problems ofthe standard perturbative calculations for light and massless fields, wegeneralize to the $O(N)$ theory a systematic method introduced previously for asingle field, which treats the zero modes exactly and the nonzero modesperturbatively. We compute the two-point functions taking into account not onlythe leading infrared contribution, coming from the self-interaction of the zeromodes, but also corrections due to the interaction of the ultraviolet modes.For the model defined in the corresponding Lorentzian de Sitter spacetime, weobtain the two-point functions by analytical continuation. We point out that apartial resummation of the leading secular terms (which necessarily involvesnonzero modes) is required to obtain a decay at large distances for masslessfields. We implement this resummation along with a systematic double expansionin an effective coupling constant $\sqrt\lambda$ and in 1/N. We explicitlyperform the calculation up to the next-to-next-to-leading order in$\sqrt\lambda$ and up to next-to-leading order in 1/N. The results reduce tothose known in the leading infrared approximation. We also show that theycoincide with the ones obtained directly in Lorentzian de Sitter spacetime inthe large N limit, provided the same renormalization scheme is used.

$O(N)$ model in Euclidean de Sitter space: beyond the leading infrared approximation