A review is presented of the unitarity problem in modern quantum cosmology  quantum gravity theory of spatially closed worlds. Based on the usual pathintegral quantization of true physical variables, we arrive at the standard DiracWheelerDeWitt formulation of quantum cosmology, which now becomes supplemented with the algorithms for conserved probability amplitudes and thus constitutes a manifestly unitary field theory. The related issue of the manyfingered time parametrizing the unitary evolution in quantum cosmology is discussed in much detail. We also give a review of the generalized canonical quantization in relativistic gauges of Batalin, Fradkin and Vilkovisky (BFV) and show that the DiracWheelerDeWitt formalism occupies an intermediate position between quantizing the physical variables and the BFV theory. The unitarity approach, which is developed in the exact theory within the framework of the formal pathintegral quantization, is confirmed at a strictly operatorial level in the oneloop approximation of a semi classical loop expansion. In particular, the general semiclassical solution of the WheelerDeWitt equations is presented and its implications in the theory of the early inflationary Universe are considered. The prospects of the thirdorder quantization and the unification of unitary quantum cosmology with the Euclidean quantum gravity are briefly discussed.

Authors: Barvinsky A.O.  Pages: 131 Year: 1993 
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