Persistent holes in the Universe: A hierarchical topology of the cosmic mass distribution

Over scales of millions of light years, the Universe is a filigree of interconnected components of various dimensions and scales. This connected pattern, known as the Cosmic Web, consists of galaxies, intergalactic gas, and dark matter that have aggregated in an intricate wispy spatial pattern marked by dense compact clusters, elongated filaments and sheet-like walls, surrounding large near-empty void regions. A distinct feature of the Cosmic web is its intrinsic hierarchical arrangement, within which the elements of the web are ubiquitous at all density ranges and scales.

The patterns in the web have significant implications for the understanding of the growth of structures in the Universe, as well as for the understanding of formation and evolution of galaxies. As a result, the efforts to characterize the Cosmic Web has been an ongoing effort for decades now, developing and employing a range of techniques and tools, broadly based on statistical, geometric and topological concepts.

This thesis concentrates on the description and detection of patterns in the Cosmic Web by harnessing the recent state-of-art techniques developed in the field of topology, involving Homology, Persistence and Morse theory. These techniques are capable of expressing topology in a greater detail compared to traditional descriptors like Euler characteristic and Minkowski functionals. Additionally, persistence describes topology in a hierarchical fashion, which ties in to the hierarchical characteristics of the web. Based on these techniques, this thesis also presents a visualization and analysis software to detect and quantify the filamentary patterns of the Cosmic Web.