Perturbative S-matrix for massive scalar fields in global de Sitter space

TL;DR

This paper develops a perturbative S-matrix framework for massive scalar fields in global de Sitter space, ensuring unitarity, CPT invariance, and proper asymptotic states, and reveals that light fields can decay at tree level.

Contribution

It introduces a novel S-matrix formulation in de Sitter space that accounts for light fields and demonstrates unitarity and decay processes at tree level.

Findings

S-matrix is CPT invariant and de Sitter invariant

Light fields are not protected from decay at tree level

Verified properties up to second order in coupling

Abstract

We construct a perturbative S-matrix for interacting massive scalar fields in global de Sitter space. Our S-matrix is formulated in terms of asymptotic particle states in the far past and future, taking appropriate care for light fields whose wavefunctions decay only very slowly near the de Sitter conformal boundaries. An alternative formulation expresses this S-matrix in terms of residues of poles in analytically-continued Euclidean correlators (computed in perturbation theory), making it clear that the standard Minkowski-space result is obtained in the flat-space limit. Our S-matrix transforms properly under CPT, is invariant under the de Sitter isometries and perturbative field redefinitions, and is unitary. This unitarity implies a de Sitter version of the optical theorem. We explicitly verify these properties to second order in the coupling for a general cubic interaction, including both tree- and loop-level contributions. Contrary to other statements in the literature, we find that a particle of any positive mass may decay at tree level to any number of particles, each of arbitrary positive masses. In particular, even very light fields (in the complementary series of de Sitter representations) are not protected from tree-level decays.