HAMILTONIAN BFV-BRST THEORY OF CLOSED QUANTUM COSMOLOGICAL MODELS

We introduce and study a new discrete basis of gravity constraints by making use of the harmonic expansion for closed cosmological models. T he full set of constraints is split into area-preserving spatial diffe omorphisms, forming a closed subalgebra, and Virasoro-like generators. The operatorial Hamiltonian BFV-BRST quantization is performed in the framework of a perturbative expansion in the dimensionless parameter which is a positive power of the ratio of the Planck volume to the vol ume of the Universe. For the (N+1) - dimensional generalization of a s tationary closed Bianchi-I cosmology the nilpotency condition for the BRST operator is examined in the first quantum approximation. It turns out that a relationship between the dimensionality of the space and t he spectrum of matter fields emerges from the requirement of quantum c onsistency of the model.