Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology

TL;DR

This paper explores Lie symmetries of the Wheeler-DeWitt equation in Bianchi Class A cosmologies, providing a systematic way to find and classify invariant solutions based on scalar field potentials.

Contribution

It introduces a symmetry-based method to analyze quantum cosmological models with scalar fields, applicable to General Relativity and modified gravity theories.

Findings

Identified invariant solutions for different scalar potentials

Classified solutions according to symmetry properties

Provided a method to select classical solutions from quantum models

Abstract

Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider General Relativity, minimally coupled scalar field gravity and Hybrid Gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.