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

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.

33 pages, 12 figures

References in corpus (9)

• The physics of exceptional points
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Quantum Mechanics of Klein-Gordon Fields I: Hilbert Space, Localized States, and Chiral Symmetry
• Quantization of time and the big bang via scale-invariant loop gravity
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Complex tridiagonal quantum Hamiltonians and matrix continued fractions
• Quantum singularities in a solvable toy model

Cited by in corpus (2)

• Emergence and localization of exceptional points in an exactly solvable toy model
• Non-Hermitian Bose-Hubbard-like quantum models