Hamiltonian BFV-BRST theory of closed quantum cosmological models

TL;DR

This paper develops a new quantum gravity constraint basis for closed cosmological models using harmonic expansion, and performs BFV-BRST quantization, revealing relationships between space dimensionality and matter spectrum.

Contribution

It introduces a novel discrete basis for gravity constraints and applies operatorial BFV-BRST quantization to closed cosmological models, exploring quantum consistency conditions.

Findings

Identifies a new constraint basis using harmonic expansion.

Performs BFV-BRST quantization in a perturbative framework.

Discovers relationships between space dimensionality and matter spectrum.

Abstract

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