A Study on the Baryon Acoustic Oscillation with Topological Data Analysis

Kono, Kai T.; Takeuchi, Tsutomu T.; Cooray, Suchetha; Nishizawa, Atsushi J.; Murakami, Koya

doi:10.48550/arxiv.2006.02905

Cited by 9 publications

(9 citation statements)

References 66 publications

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“…Recently, we have seen a proliferation of persistent homology studies focusing on different cosmological aspects. Kono et al (2020) apply persistent homology to the study of baryonic acoustic oscillations of the galaxy distribution. The potential for inferring information on the influence of non-Gaussian primordial conditions on the large-scale matter distribution have been discussed by Feldbrugge et al (2019) and Biagetti et al (2021).…”

Section: The Connectivity and Topology Of The Cosmic Webmentioning

confidence: 99%

Topological bias: How haloes trace structural patterns in the cosmic web

Bermejo¹,

Wilding²,

Weygaert³

et al. 2022

Preprint

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We trace the overall connectivity of the cosmic web as defined by haloes in the Planck-Millennium simulation using the persistence and Betti curve analysis developed in our previous papers. We consider the presence of clustering in excess of the second-order correlation function, and investigate the extent to which the dark matter haloes reflect the intricate weblike pattern of the underlying dark matter distribution. With our systematic topological analysis we correlate local information and properties of haloes with the multi-scale geometrical environment of the cosmic web, delineated by elongated filamentary bridges and sheetlike walls that establish the connections between compact clusters at the nodes and define the boundaries of near-empty voids.We capture the multi-scale topology traced by the discrete spatial halo distribution through filtering the distance field of the corresponding Delaunay tessellation. The adaptive character of the tessellation is sensitive to the local density and perfectly outlines the local geometry. The resulting nested alpha shapes contain the complete information on the multiscale topology.After normalising second-order clustering, we find a remarkable linear relationship between halo masses and topology: haloes of different mass trace environments with different topological signature. This is topological bias, a bias that is independent of the halo clustering bias associated with the two-point correlation function. Topological bias can be viewed as an environmental structure bias. We quantify this bias through a linear relation that accounts for selection effects in the analysis and interpretation of the spatial distribution of galaxies. Using this mass-dependent scaling relation allows us to take clustering into account and determine the overall connectivity on the basis of a limited sample of galaxies. This is of particular relevance with the large upcoming galaxy surveys such as DESI, Euclid, and the Vera Rubin telescope surveys.

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Section: The Connectivity and Topology Of The Cosmic Webmentioning

confidence: 99%

Topological bias: How haloes trace structural patterns in the cosmic web

Bermejo¹,

Wilding²,

Weygaert³

et al. 2022

Preprint

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“…More recently, developments in computational topology have paved the way for extracting topological information from datasets at the level of homology (Munkres 1984;Edelsbrunner & Harer 2010;van de Weygaert et al 2011;Pranav 2015;Pranav et al 2017;Moraleda et al 2019;) and its hierarchical extension, persistent homology (Edelsbrunner & Harer 2010;Pranav et al 2017;Shivashankar et al 2016;Adler et al 2017;Heydenreich et al 2021). Topological data analysis (TDA) involving homology and persistent homology has recently started finding application in astrophysical disciplines, for example, in the context of structure identification (Shivashankar et al 2016;Xu et al 2019) and quantification of large-scale structures (Kono et al 2020;Wilding et al 2021), including detection and quantification of non-Gaussianities (Feldbrugge et al 2019;Biagetti et al 2021). Homology describes the topology of a space by identifying the holes and the topological cycles that bound them.…”

Section: Introductionmentioning

confidence: 99%

Unexpected topology of the temperature fluctuations in the cosmic microwave background

Pranav

Adler

Buchert

et al. 2019

A&A

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We study the topology generated by the temperature fluctuations of the Cosmic Microwave Background (CMB) radiation, as quantified by the number of components and holes, formally given by the Betti numbers, in the growing excursion sets. We compare CMB maps observed by the Planck satellite with a thousand simulated maps generated according to the LCDM paradigm with Gaussian distributed fluctuations. The comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33 degrees. The survey of the CMB over S 2 is incomplete due to obfuscation effects by bright point sources and other extended foreground objects like our own galaxy. To deal with such situations, where analysis in the presence of "masks" is of importance, we introduce the concept of relative homology. The parametric χ 2 -test shows differences between observations and simulations, yielding p-values at per-cent to less than per-mil levels roughly between 2 to 7 degrees, with the difference in the number of components and holes peaking at more than 3σ sporadically at these scales. The highest observed deviation between the observations and simulations for b 0 and b 1 is approximately between 3σ-4σ at scales of 3 to 7 degrees. There are reports of mildly unusual behaviour of the Euler characteristic at 3.66 degrees in the literature, computed from independent measurements of the CMB temperature fluctuations by Planck's predecessor WMAP (Wilkinson Microwave Anisotropy Probe) satellite. The mildly anomalous behaviour of Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and the first Betti numbers, respectively. Further, since these topological descriptors show anomalous behaviour consistently over independent measurements of Planck and WMAP, instrumental errors and systematics may be an unlikely source. These are also the scales at which the observed maps exhibit low variance compared to the simulations, and approximately the range of scales at which the power spectrum exhibits a dip with respect to the theoretical model. Non-parametric tests show even stronger differences at almost all scales. Crucially, Gaussian simulations, based on power spectrum matching the characteristics of the observed dipped power spectrum, are not able to resolve the anomaly. Understanding the origin of the anomalies in the CMB -whether cosmological in nature, or arising due to late-time effects is an extremely challenging task. Regardless, beyond the trivial possibility that this may still be a manifestation of an extreme Gaussian case, these observations, along with the super-horizon scales involved, may motivate to look at primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology.

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“…Recently, Kimura & Imai (2017) determined persistence diagrams for (small) volume-limited samples of the DR12 release of the SDSS galaxy redshift survey in an attempt to characterize the topology of the spatial galaxy distribution, while Xu et al (2019) used persistence to identify individual voids and filaments in heuristic models of the cosmic matter distribution (also see Shivashankar et al 2016). Kono et al (2020) applied topological data analysis towards studying baryonic acoustic oscillations in the galaxy distribution, while Biagetti et al (2020) studied persistence properties of the large scale matter distribution in cosmologies with non-Gaussian primordial conditions (also see Feldbrugge et al 2019). The explicit application of homology measures in the study of the primordial temperature perturbations in the cosmic microwave background are reported in Pranav et al (2019b) and Adler et al (2017).…”

Section: This Study: Persistent Topology Of the Cosmic Webmentioning

confidence: 99%

Persistent homology of the cosmic web. I: Hierarchical topology in $Λ$CDM cosmologies

Wilding,

Nevenzeel,

van de Weygaert

et al. 2020

Preprint

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Using a set of ΛCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features.The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established.The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

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A Study on the Baryon Acoustic Oscillation with Topological Data Analysis

Cited by 9 publications

References 66 publications

Topological bias: How haloes trace structural patterns in the cosmic web

Topological bias: How haloes trace structural patterns in the cosmic web

Unexpected topology of the temperature fluctuations in the cosmic microwave background

Persistent homology of the cosmic web. I: Hierarchical topology in $Λ$CDM cosmologies

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