Oral Abstract

Oral Contribution (O0.7) Georg Wilding (Kapteyn Astronomical Institute)

Persistent homology of the cosmic web: Hierarchical topology in LCDM cosmologies

Using a set of LCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features.
The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established.
Features of the diagrams are intimately related to key transitions in the structure formation process, such as the detachment of matter concentrations from the Hubble expansion and their beginning collapse. We find a significantly higher and more profound level of information on the structure formation process in persistence diagrams than in more global summary statistics like Euler characteristic or Betti numbers.