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

TL;DR

The paper develops an observer-centric S-matrix framework for interacting scalars in four-dimensional de Sitter spacetime, computing amplitudes in the $SO(1,4)$ angular-momentum basis and using a BD vacuum. It derives a new integral representation for the Feynman propagator and demonstrates infrared finiteness at tree level, along with the absence of kinematic singularities except for conformally coupled scalars. The authors find no stable particles, with decay rates exponentially suppressed for masses above the de Sitter scale, and show that vacuum-to-multiparticle production vanishes, indicating BD vacuum stability under matter interactions. In the large-mass/momentum limit, de Sitter amplitudes reproduce flat-space results, while curvature provides an infrared cutoff in the deep infrared, motivating extensions to spinning, gauge, and gravitational interactions.

Abstract

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.

Figures (3)

• Figure 1: Mass dependence of one to two particle decays. All particles with ${\bm{L}}=0$.
• Figure 2: Angular momentum dependence of one to two particle decays. All particles with $\mu=0$.
• Figure 3: $\bm{t}$-channel exchange diagram.