Quantum cosmological perfect fluid model and its classical analogue

The quantization of gravity coupled to a perfect fluid model leads to a Schr\"odinger-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 $p = \alpha\rho$; 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 $\alpha$, 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.Comment: Latex file, 13 page

A Fluid Generalization of Membranes

In a certain sense a perfect fluid is a generalization of a point particle. This leads to the question as to what is the corresponding generalization for extended objects. The lagrangian formulation of a perfect fluid is much generalized and this has as a particular example a fluid which is a classical generalization of a membrane, however there is as yet no indication of any relationship between their quantum theories.Comment: To appear in CEJP, updated to coincide with published versio