Causal dynamical triangulations (CDT) is a sum-over-histories approach to quantum gravity which leverages the techniques developed in lattice quantum field theory. In this talk, I discuss the thick sandwich problem in CDT: Given initial and final spacelike hypersurfaces, each with a fixed geometry, what is the transition amplitude for one transitioning into the other? And what geometries dominate the associated path integral? I discuss preliminary studies performed in this direction. I also highlight open problems and interesting directions for future research.
In this work we consider a recent proposal in which gravitational interactions are mediated via the exchange of classical information and apply it to a quantized Friedman-Robertson-Walker (FRW) universe with the assumption that any test particles must feel a classical metric. We show that such a model results in decoherence in the FRW state that manifests itself as a dark energy fluid that fills the spacetime. Motivated by quantum-classical interactions this model is yet another example of theories with violation of energy-momentum conservation whose signature could have significant consequences for the observable universe.
