Quantum Big Bang without fine-tuning in a toy-model

Abstract

The question of possible physics before Big Bang (or after Big Crunch) is addressed via a schematic non-covariant simulation of the loss of observability of the Universe. Our model is drastically simplified by the reduction of its degrees of freedom to the mere finite number. The Hilbert space of states is then allowed time-dependent and singular at the critical time $t=t_c$. This option circumvents several traditional theoretical difficulties in a way illustrated via solvable examples. In particular, the unitary evolution of our toy-model quantum Universe is shown interruptible, without any fine-tuning, at the instant of its bang or collapse $t=t_c$.

20 pp., 1 fig., invited talk for the conference "10th Workshop on Quantization, Dualities and Integrable Systems" (April 22 - 24, 2011), http://qdis.emu.edu.tr/index.html

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Cited by in corpus (9)

• Non-Hermitian interaction representation and its use in relativistic quantum mechanics
• Quantum catastrophes: a case study
• Crypto-unitary forms of quantum evolution operators
• Three solvable matrix models of a quantum catastrophe
• Wheeler-DeWitt equation and the applicability of crypto-Hermitian interaction representation in quantum cosmology
• Solvable non-Hermitian discrete square well with closed-form physical inner product
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• New Concept of Solvability in Quantum Mechanics
• Coulomb potential and the paradoxes of PT-symmetrization