Generalized uncertainty principle and the conformally coupled scalar field quantum cosmology

TL;DR

This paper solves the Wheeler-DeWitt equation for a quantum cosmological model with a conformally coupled scalar field under a generalized uncertainty principle, revealing singularity-free wave packets that follow classical trajectories.

Contribution

It provides an exact solution to the Wheeler-DeWitt equation incorporating a generalized uncertainty principle in quantum cosmology.

Findings

Wave packets closely follow classical trajectories.

Wave packets exhibit singularity-free behavior.

Constructed wave packets strongly peaked on classical paths.

Abstract

We exactly solve the Wheeler-DeWitt equation for the closed homogeneous and isotropic quantum cosmology in the presence of a conformally coupled scalar field and in the context of the generalized uncertainty principle. This form of generalized uncertainty principle is motivated by the black hole physics and it predicts a minimal length uncertainty proportional to the Planck length. We construct wave packets in momentum minisuperspace which closely follow classical trajectories and strongly peak on them upon choosing appropriate initial conditions. Moreover, based on the DeWitt criterion, we obtain wave packets that exhibit singularity-free behavior.