EQUILIBRIUM STATE OF A SELF-INTERACTING SCALAR FIELD IN THE DE SITTERBACKGROUND

The behavior of a weakly self-interacting scalar field with a small ma ss in the de Sitter background is investigated using the stochastic ap proach (including the case of a double-well interaction potential). Th e existence of the de Sitter-invariant equilibrium quantum state of th e scalar field in the presence of the interaction is shown for any sig n of the mass term. The stochastic approach is further developed to pr oduce a method of calculating an arbitrary anomalously large correlati on function of the scalar field in the de Sitter background, and expre ssions for the two-point correlation function in the equilibrium state , correlation time, and spatial physical correlation radius are presen ted. The latter does not depend on time, which implies that the charac teristic size of domains with positive and negative values of the scal ar field remains the same on average in the equilibrium state in spite of the expansion of the t=const hypersurface of the de Sitter space-t ime.