Tessellating the Universe: the Zel'dovich and Adhesion tiling of space

TL;DR

This paper explores a geometrical model of the universe's large-scale structure using tessellations derived from the adhesion approximation, linking cosmic features to mathematical elements like vertices and edges.

Contribution

It introduces a tessellation-based framework for understanding cosmic structure formation, connecting mathematical tessellations with astronomical objects and their evolution.

Findings

Vertices correspond to galaxy clusters and contain most mass.

Filaments are represented as edges with significant mass.

Voids are modeled as faces and tiles, being less massive.

Abstract

The adhesion approximation is a simple analytical model suggested for explanation of the major geometrical features of the observed structure in the galaxy distribution on scales from 1 to (a few)x100/h Mpc. It is based on Burgers' equation and therefore allows analysis in considerable detail. A particular version of the model that assumes the infinitesimal viscosity naturally results in irregular tessellation of the universe. Generic elements of the tessellation: vertices, edges, faces and three-dimensional tiles can be associated with astronomical objects of different kinds: clusters, superclusters and voids of galaxies. Point-like vertices contain the most of the mass and one-dimensional edges (filaments) are the second massive elements. The least massive are the two-dimensional faces and tiles (voids). The evolution of the large-scale structure can be viewed as a continuous process that transports mass predominantly from the high- to low-dimensional elements of the tessellation. For instance, the mass from the cells flows into faces, edges and vertices, in turn the mass from faces flows into edges and vertices, etc. At the same time, the elements of the tessellation themselves are in continuous motion resulting in mergers of some vertices, growth of some tiles and shrinking and disappearance of the others as well as other metamorphoses.