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