Massless Interacting Scalar Fields in de Sitter space

We present a method to compute the two-point functions for an O(N) scalar field model in de Sitter spacetime, avoiding the well known infrared problems for massless fields. The method is based on an exact treatment of the Euclidean zero modes and a perturbative one of the nonzero modes, and involves a partial resummation of the leading secular terms. This resummation, crucial to obtain a decay of the correlation functions, is implemented along with a double expansion in an effective coupling constant √λ and in 1/N. The results reduce to those known in the leading infrared approximation and coincide with the ones obtained directly in Lorentzian de Sitter spacetime in the large N limit. The new method allows for a systematic calculation of higher order corrections both in √λ and in 1/N