On the conformally coupled scalar field quantum cosmology

TL;DR

This paper introduces a new initial condition for quantum cosmology with a conformally coupled scalar field, providing exact solutions and demonstrating a strong classical-quantum correspondence through wave packets and Bohmian trajectories.

Contribution

It presents a novel initial condition and exact solutions for conformally coupled scalar field quantum cosmology, linking classical and quantum descriptions.

Findings

Wave packets follow classical trajectories closely.

Quantum potential vanishes along Bohmian paths.

Model exhibits singularities at quantum level.

Abstract

We propose a new initial condition for the homogeneous and isotropic quantum cosmology, where the source of the gravitational field is a conformally coupled scalar field, and the maximally symmetric hypersurfaces have positive curvature. After solving corresponding Wheeler-DeWitt equation, we obtain exact solutions in both classical and quantum levels. We propose appropriate initial condition for the wave packets which results in a complete classical and quantum correspondence. These wave packets closely follow the classical trajectories and peak on them. We also quantify this correspondence using de-Broglie Bohm interpretation of quantum mechanics. Using this proposal, the quantum potential vanishes along the Bohmian paths and the classical and Bohmian trajectories coincide with each other. We show that the model contains singularities even at the quantum level. Therefore, the resulting wave packets closely follow the classical trajectories from big-bang to big-crunch.