Abstract
Underdense regions in the cosmic mass distribution expand with respect to the background and become more and more spherical. This physical mechanism produces a geometrical model, Voronoi foam, for the asymptotic distribution (“skeleton”) of the cosmic mass on 10–200 Mpc scales. Voronoi foam is a packing of polyhedral cells uniquely determined by the sites of the initial underdense regions. The walls are identified as the pancakes, the edges as the filaments, and the vertices as the clusters in the galaxy distribution.
The Voronoi tessellation is a good model for the galaxy distribution on megaparsec scales. It does not describe that distribution on small scales, but it forms a useful complement to N-body techniques, which have a low dynamic range in wavenumber space, and which suffer from sampling noise and boundary effects on very large scales. The Voronoi model enables one to study, in arbitrary detail, what the consequences of a cellular galaxy distribution are.
The correlation function of the vertices in the Voronoi tessellation is a power law with a slope and amplitude totally in accordance with the observed cluster-cluster correlation, indicating that this function could be due to cellular geometry of the galaxy distribution on megaparsec scales, rather than to the dynamics of these structures.
The Voronoi model has one failing in common with other theories of cosmic structure formation: the implied fluctuations of the microwave background are too large, unless the usual fudging is applied. For a complete review of this subject, see Icke & Van de Weygaert (1991).
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Icke, V. (1994). The Galaxy Distribution as a Voronoi Foam. In: Bosetti, P.C. (eds) Trends in Astroparticle-Physics. TEUBNER-TEXTE zur Physik, vol 28. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-01466-9_8
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