Darboux parameter for empty FRW quantum universes and quantum cosmological singularities

TL;DR

This paper explores the factorization of the Wheeler-DeWitt equation in vacuum FRW quantum universes, introducing a Darboux parameter that characterizes quantum singularities and their positions in the cosmological model.

Contribution

It presents a novel application of supersymmetric methods to factorize the Wheeler-DeWitt equation, revealing a new class of singular wavefunctions parameterized by a Darboux constant.

Findings

Introduces a Darboux parameter as a Riccati integration constant.

Defines a class of singular wavefunctions in quantum cosmology.

Links the Darboux parameter to the physical position of singularities.

Abstract

I present the factorization(s) of the Wheeler-DeWitt equation for vacuum FRW minisuperspace universes of arbitrary Hartle-Hawking factor ordering, including the so-called strictly isospectral supersymmetric method. By the latter means, one can introduce an infinite class of singular FRW minisuperspace wavefunctions characterized by a Darboux parameter that mathematically speaking is a Riccati integration constant, while physically determines the position of these strictly isospectral singularities on the Misner time axis