On the evolution of Betti curves in the Cosmic web

Abstract

In this work, we study the evolution of Betti curves obtained by persistent-homological analysis of point clouds formed by halos in different cosmological $N$-body simulations. We show that they can be approximated with a scaled log-normal distribution function with reasonable precision. Our analysis shows that the shapes and maximums of Betti curves exhibit dependence on the mass range of the selected subpopulation of halos. Still, at the same time, the resolution of a simulation does not play any significant role, provided that the mass distribution of simulated halos is complete down to a given mass scale. Besides, we study how Betti curves change with the evolution of the Universe, i.e., their dependence on redshift. Sampling subpopulations of halos within certain mass ranges up to redshift $z=2.5$ yields a surprisingly small difference between corresponding Betti curves. We propose that this may be an indicator of the existence of a new specific topological invariant in the structure of the Universe.

21 pages, 8 figures

References in corpus (26)

• Planck 2015 results. XIII. Cosmological parameters
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Halos and galaxies in the standard cosmological model: results from the Bolshoi simulation
• The persistent cosmic web and its filamentary structure I: Theory and implementation
• Halo concentrations in the standard LCDM cosmology
• The persistent cosmic web and its filamentary structure II: Illustrations
• The Halo Mass Function: High-Redshift Evolution and Universality
• Shapefinders: A new shape diagnostic for large scale structure
• The Topology of the Cosmic Web in Terms of Persistent Betti Numbers
• On the connectivity of the cosmic web: theory and implications for cosmology and galaxy formation
• Felix: A Topology based Framework for Visual Exploration of Cosmic Filaments
• Measuring the Geometry and Topology of Large Scale Structure using SURFGEN: Methodology and Preliminary Results
• Weak Lensing Light-Cones in Modified Gravity simulations with and without Massive Neutrinos
• Betti numbers of Gaussian fields
• Euclid Preparation. XXVIII. Forecasts for ten different higher-order weak lensing statistics
• Finding cosmic voids and filament loops using topological data analysis
• Persistent homology in cosmic shear: constraining parameters with topological data analysis
• Measuring the topology of reionization with Betti numbers
• Stochastic Homology of Gaussian vs. non-Gaussian Random Fields: Graphs towards Betti Numbers and Persistence Diagrams
• Persistent homology of the cosmic web. I: Hierarchical topology in $\Lambda$CDM cosmologies
• Persistent Homology and Non-Gaussianity
• Persistent topology of the reionisation bubble network. I: Formalism & Phenomenology
• Persistent topology of the reionization bubble network. II: Evolution & Classification
• Probing Dark Energy with Alpha Shapes and Betti Numbers
• Wasserstein distance as a new tool for discriminating cosmologies through the topology of large scale structure
• Topological data analysis reveals differences between simulated galaxies and dark matter haloes