Counting voids and filaments: Betti Curves as a Topological Probe for Cosmology

arXiv:2512.07236 · astro-ph.CO · Submitted 2025-12-08 · Read on arXiv

astro-ph.CO

Submitted: 2025-12-08

Updated: 2026-09-08

Comments: 25 pages, 17 figures, published in PRD

DOI: 10.1103/1c23-8l95

Code: https://github.com/ajouellette/alpha_complex_wrapper

Project page: https://johannesbuchner.github.io/UltraNest

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Persistent Homology — 12× in this paper · explained in 3 episodes
• alpha — 12× in this paper · explained in 1 episode
• Clustering — 9× in this paper · explained in 2 episodes
• Accuracy — 8× in this paper · explained in 1 episode
• Robustness — 8× in this paper · explained in 5 episodes
• Bayesian Inference — 6× in this paper · explained in 5 episodes
• Bispectrum — 4× in this paper · explained in 3 episodes
• Core — 4× in this paper · explained in 2 episodes
• Degeneracy — 4× in this paper · explained in 3 episodes
• Modified Gravity — 4× in this paper
• Non-Gaussianity — 4× in this paper · explained in 2 episodes
• Trace — 4× in this paper · explained in 2 episodes
• Abundance — 3× in this paper · explained in 1 episode
• Feature Engineering — 3× in this paper · explained in 3 episodes
• Persistence Diagram — 3× in this paper
• Primordial non-Gaussianity — 3× in this paper · explained in 2 episodes
• Void Size Function — 3× in this paper
• Baryon Acoustic Oscillations — 2× in this paper
• Bayesian Optimization — 2× in this paper · explained in 3 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Feature Selection — 2× in this paper · explained in 4 episodes
• Meta-learning — 2× in this paper · explained in 2 episodes
• Redshift-Space Distortions (RSD) — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Alignment — 1× in this paper · explained in 1 episode
• Bayesian Framework — 1× in this paper · explained in 3 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Benchmarking — 1× in this paper · explained in 3 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Higher-order statistics — 1× in this paper · explained in 2 episodes
• Independent Component Analysis — 1× in this paper
• Interpretability — 1× in this paper · explained in 15 episodes
• Matter Power Spectrum — 1× in this paper · explained in 2 episodes
• Model-Agnostic — 1× in this paper · explained in 2 episodes
• Modified Gravity (MG) — 1× in this paper · explained in 2 episodes
• Point Cloud Data — 1× in this paper · explained in 2 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Resident Set Size — 1× in this paper
• Signal-to-noise ratio (SNR) — 1× in this paper · explained in 2 episodes
• Velocity Dispersion — 1× in this paper · explained in 2 episodes

Sources

• The 2dF Galaxy Redshift Survey: Final Data Release
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogs for Cosmological Analysis
• The Baryon Oscillation Spectroscopic Survey of SDSS-III
• The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological Implications from two Decades of Spectroscopic Surveys at the Apache Point observatory
• The Early Data Release of the Dark Energy Spectroscopic Instrument
• How Filaments are Woven into the Cosmic Web
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints
• MUltiplexed Survey Telescope (MUST) Science White Paper I: Overview of Large-Scale Structure Cosmology in the Era of Stage-V Spectroscopic Surveys
• The Spectroscopic Stage-5 Experiment
• The Wide-field Spectroscopic Telescope (WST) Science White Paper
• DESI 2024 V: Full-Shape Galaxy Clustering from Galaxies and Quasars
• Planck 2018 results. IV. Diffuse component separation
• Cosmological Constraints using the Void Size Function Data from BOSS DR16
• Robust Morphological Measures for Large-Scale Structure in the Universe
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions
• Minkowski Functionals of Large-Scale Structure as a Probe of Modified Gravity
• Topological Data Analysis
• An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists

Related papers

• Angular clustering and bias of photometric quasars in the Kilo-Degree Survey Data Release 4
• A Novel kinetic Sunyaev-Zel'dovich Estimator for Electron-Electron Correlations
• Magnetic fields at the dawn of structure formation I. The CARLA J1510+5958 proto-cluster
• Dark Energy Survey Year 6 Results: Weak Lensing and Galaxy Clustering Cosmological Analysis Framework
• Exploring the Impact of Systematic Bias in Type Ia Supernova Cosmology Across Diverse Dark Energy Parametrizations
• Non-Gaussian Galaxy Stochasticity and the Noise-Field Formulation