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In the first moments, the Universe was squeezed to tiny sizes. What keeps it from collapsing entirely into a point? One answer comes from quantum mechanics: the wave function describes all possible states, and particles move along hidden trajectories that depend on the shape of this wave.

The authors took two simple shapes of wave packets — Gaussian (bell-shaped) and Lorentzian (with a long power-law tail). For each, they computed trajectories in mini-superspace — a simplified model of the Universe with flat symmetry. The Gaussian wave almost always leads to classical collapse into a singularity: only a small fraction of trajectories make small cycles. The Lorentzian wave, on the contrary, creates a strong quantum potential barrier and a rich velocity field, so a significant portion of trajectories experience a bounce and avoid singularity over a wide range of volumes.

Then they checked how quickly the probability distribution reaches equilibrium, as predicted by Born's rule. For the Gaussian wave, the trajectory flow is laminar: they accumulate near boundaries and do not mix, so the H-function (a measure of deviation from equilibrium) decreases non-monotonically and gets stuck at a nonzero level. The Lorentzian wave gives complex trajectories, monotonic decrease of the H-function, and better, though still incomplete, approximation to equilibrium.

It turns out that the very structure of the wave packet governs both the fate of the singularity and the speed of forgetting initial conditions. A Universe with a "heavy tail" in the wave function not only bounces more often but also reaches a typical quantum state faster. This is a step toward understanding why our world looks classical, even though quantum uncertainty lies at its core.