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We examine long-wavelength correlation functions of massive scalar fields inde Sitter spacetime. For the theory with a quartic self-interaction, thetwo-point function is calculated up to two loops. Comparing our results withthe Hartree-Fock approximation and with the stochastic approach shows that theformer resums only the cactus type diagrams, whereas the latter contains thesunset diagram as well and produces the correct result. We also demonstratethat the long-wavelength expectation value of the commutator of two fields isequal to zero both for spacelike and timelike separated points.

Massive scalar field in de Sitter spacetime: a two-loop calculation and a comparison with the stochastic approach