  We consider the question of asymptotic observables in cosmology. We assume
that string theory contains a landscape of vacua, and that metastable de Sitter
regions can decay to zero cosmological constant by bubble nucleation. The
asymptotic properties of the corresponding bounce solution should be
incorporated in a nonperturbative quantum theory of cosmology. A recent
proposal for such a framework defines an S-matrix between the past and future
boundaries of the bounce. We analyze in detail the properties of asymptotic
states in this proposal, finding that generic small perturbations of the
initial state cause a global crunch. We conclude that late-time amplitudes
should be computed directly. This would require a string theory analogue of the
no-boundary proposal.
