The simplest possible bouncing quantum cosmological model

TL;DR

This paper develops a simple quantum cosmological bouncing model using the trajectory formulation of quantum mechanics, allowing for non-symmetric and multiple bounces, and extends it to include shear effects via Bianchi I quantization.

Contribution

It introduces a more general class of Gaussian wave functions in a bouncing quantum cosmological model, enabling non-symmetric and multiple bounce solutions, and incorporates shear through Bianchi I quantization.

Findings

Non-symmetric bounce solutions are possible.

Multiple bounces can occur naturally in the model.

Shear effects can be included via Bianchi I quantization.

Abstract

We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the FLRW minisuper- space without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice con- sisting of modified Gaussian wave functions, aiming at obtaining a non singular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperpace.