SO(4) Invariant States in Quantum Cosmology

TL;DR

This paper investigates linearisation instability in quantum cosmology models, demonstrating that constraints enforce SO(4) invariance on wave functions in perturbative mini-superspace models with $S^3$ spatial sections.

Contribution

It explicitly shows that second-order constraints in perturbed quantum cosmology models require wave functions to be SO(4) invariant, clarifying the role of symmetry in these models.

Findings

Constraints enforce SO(4) invariance of wave functions.

Linearisation instability affects perturbative quantum cosmology.

Wave functions must satisfy specific symmetry conditions.

Abstract

The phenomenon of linearisation instability is identified in models of quantum cosmology that are perturbations of mini-superspace models. In particular, constraints that are second order in the perturbations must be imposed on wave functions calculated in such models. It is shown explicitly that in the case of a model which is a perturbation of the mini-superspace which has $S^3$ spatial sections these constraints imply that any wave functions calculated in this model must be SO(4) invariant. (This replaces the previous corrupted version.)