Asymptotic states of the bounce geometry

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.