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

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