Voronoi Tessellations and the Cosmic Web: Spatial Patterns and Clustering across the Universe

TL;DR

This paper explores how Voronoi tessellations can model the large-scale foamlike structure of the universe, revealing insights into cosmic clustering and spatial patterns.

Contribution

It demonstrates the application of Voronoi tessellations to describe and analyze the cosmic web's spatial distribution and clustering properties.

Findings

Voronoi tessellations effectively model the foamlike cosmic structure.

Clustering strength and extent scale with the tessellation nodes.

Cellular patterns may cause intrinsic geometric clustering.

Abstract

The spatial cosmic matter distribution on scales of a few up to more than a hundred Megaparsec displays a salient and pervasive foamlike pattern. Voronoi tessellations are a versatile and flexible mathematical model for such weblike spatial patterns. They would be the natural asymptotic result of an evolution in which low-density expanding void regions dictate the spatial organization of the Megaparsec Universe, while matter assembles in high-density filamentary and wall-like interstices between the voids. We describe the results of ongoing investigations of a variety of aspects of cosmologically relevant spatial distributions and statistics within the framework of Voronoi tessellations. Particularly enticing is the finding of a profound scaling of both clustering strength and clustering extent for the distribution of tessellation nodes, suggestive for the clustering properties of galaxy clusters. Cellular patterns may be the source of an intrinsic ``geometrically biased'' clustering.