Bohmian singularity resolution and quantum relaxation in Bianchi type-I quantum cosmology

We investigate cosmological singularity resolution and relaxation dynamics within the Bohmian mechanics via the plane-symmetric Bianchi type-I minisuperspace model in the Wheeler-DeWitt framework of quantum cosmology by constructing wave functions as Gaussian and Lorentzian wavepackets. Our analyses of the corresponding Bohmian trajectories reveal that Gaussian superposition predominantly yields classical singular solutions, with only a low fraction of small-amplitude cyclic trajectories. On the other hand, the Lorentzian wavepacket, characterized by the power-law momentum tail, generates stronger quantum potential barrier and a substantially rich velocity field, producing a significant fraction of non-singular bounce trajectories over extended volume ranges. We further examine quantum relaxation by evolving non-equilibrium distributions under the corresponding guidance dynamics. The Gaussian superposition exhibits laminar flow leading to boundary accumulation and incomplete relaxation, with non-monotonic decay of the $H$-function followed by saturation. In contrast, the Lorentzian wavepacket induces more complex trajectories, yielding monotonic decay of the $H$-function and better, though still incomplete, approach to Born-rule equilibrium. These results demonstrate that the inherent structure of the wave packet governs both singularity resolution and quantum relaxation through the nature of the Bohmian velocity field.

💡 Research Summary

The paper addresses two central issues in quantum gravity—resolution of cosmological singularities and the dynamical relaxation toward the Born rule—by employing the de Broglie‑Bohm (pilot‑wave) formulation of quantum mechanics in a minisuperspace setting. The authors focus on the plane‑symmetric Bianchi I model, whose metric can be written in terms of two logarithmic variables: α = ln(a²b) representing the overall volume and β = ½ ln(b²/a²) encoding anisotropy. After canonical quantization, the Wheeler–DeWitt (WDW) equation reduces to a simple hyperbolic form ∂²αΨ − ∂²βΨ = 0. By separating variables, the general solution is expressed as an integral over a mode‑parameter k: Ψ(α,β)=∫F(k)