Quote as: Tozzi A. 2019. Is cosmic homogeneity correlated with hyperuniform dynamics? (electronic response to: Klatt MA, Lovrić J, Chen D, Kapfer SC, Schaller FM, et al. 2019. Universal hidden order in amorphous cellular geometries. NATURE COMMUNICATION, 10: 811).
In a scenario alternative to inflationary expansion, we are allowed to describe the cosmic evolution suddenly after the Big Bang in terms of Lloyd iterations, where the initial quantum seeds stand for initial point sets, progressively converted to point sets with a centroidal Voronoi diagram. In other words, the tiny perturbations in the primordial universe which seed the later formation of cosmic macro-structures might stand for the starting points of the subsequent processes described in terms of Voronoi cells. This would permit us to achieve, starting from countless different possible conformations of the primeval Universe, the required isotropic and homogeneous Cosmic Background Radiation. Indeed, after just 10^5 iterations, every possible initial system must converge towards an hyperuniform state, where the energy is very low and the degree of uniformity very high.