Light fields in various patches of de Sitter spacetime

We start with the consideration of the loop effects for light fields with nonzero mass in the expanding Poincaré patch of de Sitter spacetime. We derive the Dyson-Schwinger equation, which sums up the leading infrared (growing with time) loop corrections in certain limit for small initial perturbations above the Bunch-Davies state. The solution of this equation shows the destiny of the initial state at the future infinity. Then we discuss the case of the contracting Poincaré patch and global de Sitter spacetime and briefly the case of different initial conditions in the expanding Poincaré patch.