Decoherence Functionals for Quantum Cosmology

Decoherence functionals are explicitly constructed for flat cosmological models in both standard Wheeler-DeWitt theory and also loop quantum cosmology, thereby permitting consistent quantum predictions to be made in complete, mathematically precise models of quantum cosmology. Consistent families of quantum histories are exhibited and the prediction of semiclassical behavior for suitable initial states described. Criteria for the resolution of the initial singularity are formulated in a precise way. Singularity avoidance in loop-quantized models is contrasted with the failure of Wheeler-DeWitt quantum cosmological models to avoid the big-bang singularity. The critical role played by decoherence of histories is illustrated in this example by showing that failure to consider decoherence leads to precisely the \emph{opposite} conclusion for a large class of states.