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We compute the four-point correlation function of a light O(N) scalar field in de Sitter space in the large-N limit. For superhorizon momentum modes, infrared effects strongly enhance the size of loop contributions. We find that in the deep infrared limit, the latter are of the same order as the tree-level one. The tree-level momentum structure, characteristic of a contact term, gets renormalized by a factor of order unity. In addition loop contributions give rise to a new momentum structure, characteristic of an exchange diagram, corresponding to the exchange of an effective composite scalar degree of freedom.
Julien Serreau (2013) studied this question.