Infrared correlations in de Sitter space: Field theoretic versus stochastic approach

We consider massive λφ4 theory in de Sitter background. The mass of the scalar field φ is chosen small enough, such that the amplification of superhorizon momentum modes leads to a significant enhancement of infrared correlations, but large enough such that perturbation theory remains valid. Using the closed-time-path approach, we calculate the infrared corrections to the two-point function of φ to two-loop order. To this approximation, we find agreement with the correlation found using stochastic methods. When breaking the results down to individual Feynman diagrams obtained by the two different methods, we observe that these agree as well.