Few-grid-point simulations of Big Bang singularity in quantum cosmology

TL;DR

This paper explores quantum models supporting a point-like Big Bang, analyzing singularity behavior and the implications of exceptional points, to bridge classical and quantum gravity approaches.

Contribution

It introduces exactly solvable pseudo-Hermitian quantum models that support a point-like Big Bang and examines the singularity's unfolding using exceptional points.

Findings

Singular values of observables are useful in analyzing the Big Bang singularity.

The models support a point-like Big Bang scenario within quantum cosmology.

Ambiguity in the unfolding of the singularity after Big Bang is demonstrated.

Abstract

In the context of the current lack of compatibility of the classical and quantum approaches to gravity, exactly solvable elementary pseudo-Hermitian quantum models are analyzed supporting the acceptability of a point-like form of Big Bang. The purpose is served by a hypothetical (non-covariant) identification of the ``time of Big Bang'' with the Kato's exceptional-point parameter $t=0$. Consequences (including the ambiguity of the patterns of unfolding of the singularity after Big Bang) are studied in detail. In particular, singular values of the observables are shown useful in the analysis.