Isometric Evolution in de Sitter Quantum Gravity

Do the postulates of quantum mechanics survive in quantum gravity?  The probabilistic interpretation of amplitudes, enforced by the unitarity of time evolution, is not guaranteed within the path integral formulation and has to be checked.  Leveraging the gravitational path integral, we find a non-perturbative mechanism whereby a sum over smooth geometries leads to isometric rather than unitary evolution, which we demonstrate in simple models of de Sitter quantum gravity.  These models include Jackiw-Teitelboim gravity and a minisuperspace approximation to Einstein gravity with a positive cosmological constant.  In these models we find that knowledge of bulk physics, even on arbitrarily large timescales, is insufficient to deduce the de Sitter S-matrix