Quantum cosmological perfect fluid models

Abstract

Perfect fluid Friedmann-Robertson-Walker quantum cosmological models for an arbitrary barotropic equation of state $p=\alpha \rho$ are constructed using Schutz's variational formalism. In this approach the notion of time can be recovered. By superposition of stationary states, finite-norm wave-packet solutions to the Wheeler-DeWitt equation are found. The behaviour of the scale factor is studied by applying the many-worlds and the ontological interpretations of quantum mechanics. Singularity-free models are obtained for $\alpha <1$. Accelerated expansion at present requires $-1/3>\alpha >-1$.

Latex file, 12 pages. New paragraphs in the Introduction and Conclusion, and other minor corrections in the text and in some formulas. Accepted for publication in General Relativity and Gravitation

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