Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

TL;DR

This paper investigates axisymmetric quantum cosmologies with scalar fields, identifying conditional symmetries to find non-singular semiclassical geometries and exploring their physical implications.

Contribution

It introduces a method to incorporate classical conditional symmetries into quantum cosmology, leading to particular solutions of the Wheeler-DeWitt equation with potential non-singular geometries.

Findings

Most models yield non-singular semiclassical geometries.

Conditional symmetries help select specific quantum solutions.

Effective energy-momentum tensor resembles an imperfect fluid.

Abstract

In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow \cite{Christodoulakis:2012eg} and impose the operators related to the classical conditional symmetries on the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.