Modeling the quantum evolution of the universe through classical matter

TL;DR

This paper demonstrates that quantum cosmological models with nonsingular universes can be reproduced classically by exotic matter with an implicit equation of state, revealing how quantum effects modify early universe matter content.

Contribution

It shows that quantum cosmology solutions correspond to classical models with exotic matter, including negative energy components, providing a new perspective on quantum-classical correspondence.

Findings

Quantum models imply the presence of negative energy density matter.

Classical equivalent models involve two non-interacting fluids, one with negative energy.

Negative energy density is crucial for removing the classical singularity.

Abstract

It is well known that the canonical quantization of the Friedmann-Lema\^itre-Robertson-Walker (FLRW) filled with a perfect fluid leads to nonsingular universes which, for later times, behave as their classical counterpart. This means that the expectation value of the scale factor $<a>(t)$ never vanishes and, as $t\to\infty$, we recover the classical expression for the scale factor. In this paper, we show that such universes can be reproduced by classical cosmology given that the universe is filled with an exotic matter. In the case of a perfect fluid, we find an implicit equation of state (EoS). We then show that this single fluid with an implict EoS is equivalent to two non-interacting fluids, one of them representing stiff matter with negative energy density. In the case of two non-interacting scalar fields, one of them of the phantom type, we find their potential energy. In both cases we find that quantum mechanics changes completely the configuration of matter for small values of time, by adding a fluid or a scalar field with negative energy density. As time passes, the density of negative energy decreases and we recover the ordinary content of the classical universe. The more the initial wave function of the universe is concentrated around the classical big bang singularity, the more it is necessary to add negative energy, since this type of energy will be responsible for the removal of the classical singularity.