Quantum cosmological perfect fluid model and its classical analogue

TL;DR

This paper explores quantum cosmology with perfect fluids, showing that quantum effects lead to a bouncing universe and that these models have a universal classical analogue involving a repulsive stiff matter fluid.

Contribution

It demonstrates the quantum behavior of perfect fluid cosmological models and establishes their universal classical analogue with a repulsive stiff matter component.

Findings

Quantum models predict a bouncing, non-singular universe.

Quantum scenarios are equivalent to classical models with a repulsive stiff matter fluid.

Flat and non-flat cases are mathematically equivalent to free particles and harmonic oscillators, respectively.

Abstract

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.