Quantum cosmological intertwining: Factor ordering and boundary conditions from hidden symmetries

TL;DR

This paper investigates how hidden symmetries in a quantum cosmological model influence factor ordering choices and boundary conditions, revealing their interconnectedness through the analysis of a closed FLRW universe with a scalar field.

Contribution

It demonstrates that hidden symmetries in quantum cosmology can determine factor ordering and boundary conditions, providing a new perspective on gauge invariance and spectrum constraints.

Findings

Hidden $su(1,1)$ symmetries relate to factor ordering choices.

Boundary conditions are constrained by hidden symmetries.

Factor ordering and boundary conditions are interconnected in the model.

Abstract

We explore the implications of hidden symmetries present in a particular quantum cosmological setting, extending the results reported in \cite{10,11}. In more detail, our case study is constituted by a spatially closed Friedmann-Lema\^{\i}tre-Robertson-Walker universe, in the presence of a conformally coupled scalar field. The $su(1,1)$ hidden symmetries of this model, together with the Hamiltonian constraint, lead to the gauge invariance of its corresponding Bargmann indices. We subsequently show that some factor-ordering choices can be related to the allowed spectrum of Bargmann indices and hence, to the hidden symmetries. Moreover, the presence of those hidden symmetries also implies a set of appropriate boundary conditions to choose from. In summary, our results suggest that factor ordering and boundary conditions can be intertwined when a quantum cosmological model has hidden symmetries.