Our view of the universe, its origin and development has been a long, humbling sequence of misconceptions – not surprisingly so since this is perhaps the most fundamental question of all. This paper is a further attempt in trying to shed some light on this issue, and is based on the sole assumption that quantum propagation in space must obey a Lorentz-covariant continuity equation. This would seem to be perhaps the most basic assumption that can be made, and is shown to lead to an exponentially expanding universe, as observed, and also to force new quanta to be continuously created, which would thus explain the mysterious, dominating amounts of dark energy and dark matter observed in the universe. Mass-energy, diluted by the expansion, is thus in this way continuously being replenished. In the present paper, numerical simulations of this scenario are presented, which show a self-similar expansion, and in which new quanta are created all the time as the universe expands. The spatial distribution of the quanta involved is derived to be a Pareto distribution with an infinite mean free path, and which thus also continuously creates new self-similar clusters of quanta as embryos to new galaxies in regions far away from the original source.

Boltzmann’s transport equation, relativistic covariance, cosmological expansion, Pareto distribution, numerical simulations