Scalar potentials out of canonical quantum cosmology

TL;DR

This paper derives exact and semiclassical solutions to the Wheeler-DeWitt equation for a flat FRW cosmology with a scalar field and potential, analyzing their features and classical correspondence.

Contribution

It provides new exact and semiclassical solutions for the Wheeler-DeWitt equation with specific scalar potentials in quantum cosmology.

Findings

Exact solutions for certain scalar potentials obtained.

Semiclassical analysis reveals classical limit features.

Discussion of solution properties and classical correspondence.

Abstract

Using canonical quantization of a flat FRW cosmological model containing a real scalar field $\phi$ endowed with a scalar potential $V(\phi)$, we are able to obtain exact and semiclassical solutions of the so called Wheeler-DeWitt equation for a particular family of scalar potentials. Some features of the solutions and their classical limit are discussed.