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

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