Scattering of Quantum Particles in Global de Sitter Spacetime II: Scalars in Deep Infrared

We apply the S-matrix formalism developed in Part I to the interacting scalar theory in four-dimensional de Sitter spacetime. The amplitudes are computed in the angular momentum basis, appropriate to the representations of $SO(1,4)$ de Sitter symmetry group. We discuss the properties of wavefunctions in Bunch-Davies vacuum and derive a new integral representation for the Feynman propagator. We focus on deep infrared processes probing the large scale structure of spacetime, in particular on the processes that are normally forbidden by the energy-momentum conservation laws in flat spacetime. We find that there are no stable particles in self-interacting scalar field theory, but the decay rates are exponentially suppressed for particles with masses far above $\hbar/c\ell$, where $\ell$ is the de Sitter radius. We also show that the ``all out'' amplitudes describing multiparticle production from the vacuum are identically zero, hence Bunch-Davies vacuum is stable with respect to the matter interactions. We show that at the tree level, all scattering amplitudes are infrared finite, well-defined functions of quantum numbers. They have no kinematic singularities, except for the processes involving conformally coupled scalars.