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

TL;DR

This paper presents a simplified quantum toy-model that demonstrates the universe's evolution through the Big Bang or collapse without requiring fine-tuning, addressing pre- and post-Big Bang physics.

Contribution

It introduces a finite-degree-of-freedom quantum model with a time-dependent, singular Hilbert space that allows unitary evolution to be interrupted at the critical moment.

Findings

Unitary evolution can be interrupted at the Big Bang without fine-tuning.

The model simplifies complex quantum cosmology issues.

Solvable examples illustrate the approach's effectiveness.

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 $t= t_c$.