Remarks on the Wave Function of the Universe in the Dilaton Cosmology

TL;DR

This paper investigates semi-classical solutions and the wave function of the universe in dilaton cosmology, introducing new boundary conditions that relate to avoiding curvature singularities, with solutions linked to Liouville equations.

Contribution

It presents a novel boundary condition for the wave function in dilaton cosmology and derives solutions connecting to Liouville equations, extending previous models.

Findings

Wave function satisfying new boundary conditions

Reduction of Wheeler-DeWitt equation to Liouville form

Boundary conditions linked to singularity avoidance

Abstract

Motivated by previous works, we study semi-classical cosmological solutions and the wave function of the Wheeler-DeWitt equation in the Bose-Parker-Peleg model. We obtain the wave function of the universe satisfying the suitable boundary condition of the redefined fields, which has not been considered in previous works. For some limiting cases, the Wheeler-DeWitt equation is reduced to the Liouville equation with a boundary, and its solution can be described by well-known functions. The consistent requirement of the boundary condition is related to the avoidance of the curvature singularity.