Few-Grid-Point Simulations of Big Bang Singularity in Quantum Cosmology

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 the Big Bang. The purpose is served by a hypothetical (non-covariant) identification of the “time of the Big Bang” with Kato’s exceptional-point parameter t=0. The consequences (including the ambiguity of the patterns of unfolding the singularity after the Big Bang) are studied in detail. In particular, singular values of the observables are shown to be useful in the analysis.