The Boltzmann transport equation is the rigorous continuity equation for quantum propagation in space. Requiring only that this equation should be Lorentz-covariant and dispersion-free leads to an exponentially expanding universe, and also to an exponential increase with time of the number of quanta involved, which could explain the existence of the dominating proportion (95.1 %) of dark matter and dark energy observed in the universe. Simulations of the quantum propagation from the Pareto distribution and quantum duplication thus derived from Lorentz-covariance show two specific, distinct distributions: (1) dense clusters of quantum trajectories close to each other (“dark matter”?), and (2) an extensive web of extremely long trajectories (“dark energy”?) to new such clusters. The dark matter clusters thus form a large-scale distribution of galaxy-type islands separated from each other, and immersed in a dominating web of dark energy trajectories. The simulations performed also give a ratio of dark energy to dark matter in the universe, which is consistent with the ratio recently measured by the Planck Space Telescope.

Lorentz-covariant quantum propagation, particle creation, self-similar expansion, gross structure of the universe