Dilaton Quantum Cosmology with a Schrodinger-like equation

TL;DR

This paper develops a quantum cosmological model with radiation and a dilaton field, deriving a Schrödinger-like equation, and finds bouncing universe solutions using Bohmian analysis, with implications for phantom fields.

Contribution

It introduces a Schrödinger-like formulation of quantum cosmology with a dilaton and radiation, and demonstrates bouncing solutions via Bohmian trajectories, highlighting the role of phantom scalar fields.

Findings

Explicit wavepacket solution for specific ordering factor

Bouncing behavior of the universe scale factor

Phantom scalar field is essential for consistent solutions

Abstract

A quantum cosmological model with radiation and a dilaton scalar field is analysed. The Wheeler-deWitt equation in the mini-superspace induces a Schr\"odinger equation, which can be solved. An explicit wavepacket is constructed for a particular choice of the ordering factor. A consistent solution is possible only when the scalar field is a phantom field. Moreover, although the wavepacket is time dependent, a Bohmian analysis allows to extract a bouncing behaviour for the scale factor.