2001/08/22 by A. B. Batista, J. C. Fabris, S. V. B. Goncalves +1 · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1103/physrevd.65.063519
published as Phys.Rev. D65 (2002) 063519 · Latex file, 13 pages
arxiv created 2001/08/22 · arxiv updated 2009/11/30
The quantization of gravity coupled to a perfect fluid model leads to a Schrödinger-like equation, where the matter variable plays the role of time. The wave function can be determined, in the flat case, for an arbitrary barotropic equation of state p = αρ; solutions can also be found for the radiative non-flat case. The wave packets are constructed, from which the expectation value for the scale factor is determined. The quantum scenarios reveal a bouncing Universe, free from singularity. We show that such quantum cosmological perfect fluid models admit a universal classical analogue, represented by the addition, to the ordinary classical model, of a repulsive stiff matter fluid. The meaning of the existence of this universal classical analogue is discussed. The quantum cosmological perfect fluid model is, for a flat spatial section, formally equivalent to a free particle in ordinary quantum mechanics, for any value of α, while the radiative non-flat case is equivalent to the harmonic oscillator. The repulsive fluid needed to reproduce the quantum results is the same in both cases.