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 = α ρ; 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. 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 fluid1,2. The existence of this universal classical analogue may imply that this perfect fluid coupled to gravity model is not a real quantum system. 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.
Discrete and Continuum Third Quantization of Gravity