Consistent probabilities in WheelerDeWitt quantum cosmology
Abstract
We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the WheelerDeWitt quantization of a flat FriedmannRobertsonWalker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model’s Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum WheelerDeWitt universes. Within this framework, rigorous formulas are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantummechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these WheelerDeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.
 Publication:

Physical Review D
 Pub Date:
 December 2010
 DOI:
 10.1103/PhysRevD.82.123526
 arXiv:
 arXiv:1006.3837
 Bibcode:
 2010PhRvD..82l3526C
 Keywords:

 98.80.Qc;
 03.65.Yz;
 04.60.Ds;
 04.60.Kz;
 Quantum cosmology;
 Decoherence;
 open systems;
 quantum statistical methods;
 Canonical quantization;
 Lower dimensional models;
 minisuperspace models;
 General Relativity and Quantum Cosmology;
 Quantum Physics
 EPrint:
 27 pages, 4 figures. Minor revisions and updated references. Matches published version