A Study on the Baryon Acoustic Oscillation with Topological Data Analysis

Abstract

(abridged) The scale of the acoustic oscillation of baryons at the baryon-photon decoupling is imprinted on the spatial distribution of galaxies in the Universe, known as the baryon acoustic oscillation (BAO). The correlation functions and power spectrum are used as a central tool for the studies on the BAO analysis. In this work, we analyzed the spatial distribution of galaxies with a method from the topological data analysis (TDA), in order to detect and examine the BAO signal in the galaxy distribution. The TDA provides a method to treat various types of "holes" in point set data, by constructing the persistent homology (PH) group from the geometric structure of data points and handling the topological information of the dataset. We can obtain the information on the size, position, and statistical significance of the holes in the data. A particularly strong point of the persistent homology is that it can classify the holes by their spatial dimension, i.e., a 0-dim separation, 1-dim loop, 2-dim shell, etc. We first analyzed the simulation datasets with and without the baryon physics to examine the performance of the PH method. We found that the PH is indeed able to detect the BAO signal: simulation data with baryon physics present a prominent signal from the BAO, while data without baryon physics does not show this signal. Then, we applied the PH to a quasar sample at $z<1.0$ from extended Baryon Oscillation Spectroscopic Survey in Sloan Digital Sky Survey Data Release 14. We discovered a characteristic hole (a hollow shell) at a scaler $\sim 150[\mathrm{Mpc}]$. This exactly corresponds to the BAO signature imprinted in the galaxy/quasar distribution. We performed this analysis on a small subsample of 2000 quasars. This clearly demonstrates that the PH analysis is very efficient in finding this type of topological structures even if the sampling is very sparse.

arXiv comment29 pages, 13 figures

References in corpus (25)

• Baryonic Features in the Matter Transfer Function
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• Transients from Initial Conditions in Cosmological Simulations
• The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview
• Robust Morphological Measures for Large-Scale Structure in the Universe
• Analytic Minkowski Functionals of the Cosmic Microwave Background: Second-order Non-Gaussianity with Bispectrum and Trispectrum
• Analytic Expression of the Genus in Weakly Non-Gaussian Field Induced by Gravity
• Finding cosmic voids and filament loops using topological data analysis
• The invariant joint distribution of a stationary random field and its derivatives: Euler characteristic and critical point counts in 2 and 3D
• Direct Minkowski Functional analysis of large redshift surveys: a new high--speed code tested on the luminous red galaxy Sloan Digital Sky Survey-DR7 catalogue
• Testing statistics of the CMB B-mode polarization toward unambiguously establishing quantum fluctuation of vacuum
• Studying topological structure in the epoch of reionization with 3D-Minkowski functionals of 21cm line fluctuations
• Nonlinear Evolution of Genus in Primordial Random-Gaussian Density Field
• Stages of Reionization as revealed by the Minkowski Functionals
• Persistent Homology and Non-Gaussianity
• The Shape and Size distribution of HII Regions near the percolation transition
• Studying the morphology of HI isodensity surfaces during reionization using Shapefinders and percolation analysis
• Minkowski Functionals of Convergence Maps and the Lensing Figure of Merit
• New probe of departures from general relativity using Minkowski functionals
• Tensor Minkowski Functionals: first application to the CMB
• On Minkowski Functionals of CMB polarization
• Minkowski Tensors in Three Dimensions - Probing the Anisotropy Generated by Redshift Space Distortion
• Distinguishing general relativity and $f(R)$ gravity with the gravitational lensing Minkowski functionals
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: higher-order correlations revealed by germ-grain Minkowski Functionals
• Geometrical measures of non-Gaussianity generated from single field Inflationary models

Cited by in corpus (6)

• Is the Observable Universe Consistent with the Cosmological Principle?
• Persistent homology in cosmic shear II: A tomographic analysis of DES-Y1
• Cosmological Probes of Structure Growth and Tests of Gravity
• Anomalies in the topology of the temperature fluctuations in the cosmic microwave background: An analysis of the $\text{NPIPE}$ and $\text{FFP10}$ data releases
• Detecting and analysing the topology of the cosmic web with spatial clustering algorithms I: Methods
• Insights into the dependence of galaxy properties on the environment with explainable machine learning models