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.

arXiv comment33 pages, 12 figures

References in corpus (23)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Background Independent Quantum Gravity: A Status Report
• The physics of exceptional points
• Pseudo-Hermitian Representation of Quantum Mechanics
• Absence of Singularity in Loop Quantum Cosmology
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian
• Operator (quasi-)similarity, quasi-Hermitian operators and all that
• On CCC-predicted concentric low-variance circles in the CMB sky
• 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
• Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism
• Pseudo-Hermitian Quantum Mechanics with Unbounded Metric Operators
• Turning big bang into big bounce: II. Quantum dynamics
• Multiply Degenerate Exceptional Points and Quantum Phase Transitions
• Quantum phase transitions in nonhermitian harmonic oscillator
• CCC and the Fermi paradox
• Tridiagonality, supersymmetry and non self-adjoint Hamiltonians
• 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