Quantum phantom cosmology

TL;DR

This paper explores quantum cosmology models with phantom fields, solving the Wheeler-DeWitt equation exactly in some cases, and analyzing wave packet behavior near singularities, highlighting quantum effects that may avoid classical singularities.

Contribution

It provides exact solutions to the Wheeler-DeWitt equation for phantom field models and analyzes wave packet behavior, revealing quantum effects near singularities.

Findings

Wave packets disperse near the Big Rip singularity in phantom models.

Quantum solutions are regular and avoid classical singularities.

Comparison with ordinary scalar fields shows different singularity behaviors.

Abstract

We apply the formalism of quantum cosmology to models containing a phantom field. Three models are discussed explicitly: a toy model, a model with an exponential phantom potential, and a model with phantom field accompanied by a negative cosmological constant. In all these cases we calculate the classical trajectories in configuration space and give solutions to the Wheeler-DeWitt equation in quantum cosmology. In the cases of the toy model and the model with exponential potential we are able to solve the Wheeler-DeWitt equation exactly. For comparison, we also give the corresponding solutions for an ordinary scalar field. We discuss in particular the behaviour of wave packets in minisuperspace. For the phantom field these packets disperse in the region that corresponds to the Big Rip singularity. This thus constitutes a genuine quantum region at large scales, described by a regular solution of the Wheeler-DeWitt equation. For the ordinary scalar field, the Big-Bang singularity is avoided. Some remarks on the arrow of time in phantom models as well as on the relation of phantom models to loop quantum cosmology are given.