Physical meaning and consequences of the loop infrared divergences in global de Sitter space

Following Krotov and Polyakov Nucl. Phys. B849, 410 (2011), we show that in global de Sitter space its isometry is broken by the loop IR divergences for any invariant vacuum state of the massive scalars. We derive a kinetic equation in global de Sitter space that follows from the Dyson-Schwinger equation of the Schwinger-Keldysh diagrammatic technique in the IR limit and allows us to understand the physical meaning and consequences of the loop IR divergences. In many respects, the isometry breaking in global de Sitter space is similar to the one in the contracting Poincar\'e patch of de Sitter space. Hence, as a warm-up exercise we study the kinetic equation and properties of its solutions in the expanding and contracting Poincar\'e patches of de Sitter space. Quite unexpectedly, we find that under some initial conditions there is an explosive production of massive particles in the expanding Poincar\'e patch.