Hierarchical Clustering in ${\Lambda}$CDM Cosmologies via Persistence Energy

Topological Data Analysis (TDA) has emerged as a transformative approach to extract meaningful information from complex datasets, offering a lens through which to understand the data's underlying structure. Unlike traditional data analysis methods that rely on geometric or statistical measures, TDA employs tools from both computational geometry and algebraic topology to study the topological features inherent in datasets. In the context of cosmology, where the distribution of matter exhibits complex and interconnected patterns, TDA becomes a valuable tool for uncovering the underlying cosmic topology. The cosmic web, encompassing galaxies, intergalactic gas, and dark matter, exhibits an organized tendency to form structures such as galaxy clusters, filaments (thread-like structures that connect galaxy clusters), and walls, surrounded by low-density void regions (Colberg et al. [2008], Van de Weygaert and Platen [2011], Cautun et al. [2014], Wilding et al. [2021]). Within this cosmic context, large galaxy clusters aggregate into more extensive formations referred to as filaments or superclusters of galaxies Kelesis et al. [2022].