Topological data analysis and diagnostics of compressible magnetohydrodynamic turbulence

Makarenko, Irina; Bushby, P. J.; Fletcher, Andrew; Henderson, Robin; Makarenko, N. G.; Shukurov, Anvar

doi:10.1017/s0022377818000752

Cited by 6 publications

(3 citation statements)

References 52 publications

(92 reference statements)

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“…These methods are supported by the power of an elaborate and solid mathematical framework, and complement the existing methods for gleaning meaningful information out of the ever-growing cosmological data sets. It is evident that these methodologies are valuable evaluation tools from a recent proliferation of their use in the astronomical and cosmological disciplines, in a variety of contexts including structure detection and identification [271][272][273][274], including detection of BAO signals [275], statistical characterization of ISM [276], statistical characterization of cosmological fields arising from various models, and a description of associated structures [254,266,[277][278][279][280], and detection and quantification of non-Gaussianities [281][282][283].…”

Section: Topological Anomalies In the Cmbmentioning

confidence: 99%

Is the observable Universe consistent with the cosmological principle?

Aluri

Cea

Chingangbam

et al. 2023

Class. Quantum Grav.

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The Cosmological Principle (CP) -- the notion that the Universe is spatially isotropic and homogeneous on large scales -- underlies a century of progress in cosmology. It is conventionally formulated through the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) cosmologies as the spacetime metric, and culminates in the successful and highly predictive $\Lambda$-Cold-Dark-Matter ($\Lambda$CDM) model. Yet, tensions have emerged within the $\Lambda$CDM model, most notably a statistically significant discrepancy in the value of the Hubble constant, $H_0$. Since the notion of cosmic expansion determined by a single parameter is intimately tied to the CP, implications of the $H_0$ tension may extend beyond $\Lambda$CDM to the CP itself. This review surveys current observational hints for deviations from the expectations of the CP, highlighting synergies and disagreements that warrant further study. Setting aside the debate about individual large structures, potential deviations from the CP include variations of cosmological parameters on the sky, discrepancies in the cosmic dipoles, and mysterious alignments in quasar polarizations and galaxy spins. While it is possible that a host of observational systematics are impacting results, it is equally plausible that precision cosmology may have outgrown the FLRW paradigm, an extremely pragmatic but non-fundamental symmetry assumption.

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Section: Topological Anomalies In the Cmbmentioning

confidence: 99%

Is the observable Universe consistent with the cosmological principle?

Aluri

Cea

Chingangbam

et al. 2023

Class. Quantum Grav.

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“…Our program follows the steadily increasing realization in the cosmological community that homology and persistent topology offer a range of innovative tools towards the description and analysis of the complex spatial patterns that have emerged from the gravitational evolution of the cosmic matter distribution from its primordial Gaussian conditions to the intricate spatial network of the cosmic web seen in the current Universe on Megaparsec scales. In this respect, we may refer to the seminal contribution by Sousbie (2011); Sousbie et al (2011), and the recent studies applying these topological measures to various cosmological and astronomical scenarios (van de Park et al 2013;Chen et al 2015;Shivashankar et al 2016;Makarenko et al 2017;Codis et al 2018;Xu et al 2018;Cole & Shiu 2018;Makarenko et al 2018).…”

Section: Introductionmentioning

confidence: 99%

Topology and geometry of Gaussian random fields I: on Betti numbers, Euler characteristic, and Minkowski functionals

Pranav

Weygaert

Vegter

et al. 2019

Monthly Notices of the Royal Astronomical Society

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This study presents a numerical analysis of the topology of a set of cosmologically interesting three-dimensional Gaussian random fields in terms of their Betti numbers β 0 , β 1 and β 2 . We show that Betti numbers entail a considerably richer characterization of the topology of the primordial density field. Of particular interest is that Betti numbers specify which topological features -islands, cavities or tunnels -define its spatial structure.A principal characteristic of Gaussian fields is that the three Betti numbers dominate the topology at different density ranges. At extreme density levels, the topology is dominated by a single class of features. At low levels this is a Swiss-cheeselike topology, dominated by isolated cavities, at high levels a predominantly Meatball-like topology of isolated objects. At moderate density levels, two Betti number define a more Sponge-like topology. At mean density, the topology even needs three Betti numbers, quantifying a field consisting of several disconnected complexes, not of one connected and percolating overdensity.A second important aspect of Betti number statistics is that they are sensitive to the power spectrum. It reveals a monotonic trend in which at a moderate density range a lower spectral index corresponds to a considerably higher (relative) population of cavities and islands.We also assess the level of complementary information that Betti numbers represent, in addition to conventional measures such as Minkowski functionals. To this end, we include an extensive description of the Gaussian Kinematic Formula (GKF), which represents a major theoretical underpinning for this discussion.

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“…As a result, Gaussian random fields also model the large scale structure of the Universe (van de Weygaert & Bond 2008a,b), including HI signals from structures at the epoch of reionization (Mondal et al 2015). At yet smaller scales, Gaussian random fields serve as models for galactic scale magnetic fields (Makarenko et al 2017;Makarenko et al 2018).…”

Section: Gaussian Random Fieldsmentioning

confidence: 99%

Topology and geometry of Gaussian random fields II: on critical points, excursion sets, and persistent homology

Pranav¹

2021

Preprint

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This paper is second in the series, following , focused on the characterization of geometric and topological properties of 3D Gaussian random fields. We focus on the formalism of persistent homology, the mainstay of Topological Data Analysis (TDA), in the context of excursion set formalism. We also focus on the structure of critical points of stochastic fields, and their relationship with formation and evolution of structures in the universe.The topological background is accompanied by an investigation of Gaussian field simulations based on the LCDM spectrum, as well as power-law spectra with varying spectral indices. We present the statistical properties in terms of the intensity and difference maps constructed from the persistence diagrams, as well as their distribution functions. We demonstrate that the intensity maps encapsulate information about the distribution of power across the hierarchies of structures in more detailed than the Betti numbers or the Euler characteristic. In particular, the white noise (n = 0) case with flat spectrum stands out as the divide between models with positive and negative spectral index. It has the highest proportion of low significance features. This level of information is not available from the geometric Minkowski functionals or the topological Euler characteristic, or even the Betti numbers, and demonstrates the usefulness of hierarchical topological methods. Another important result is the observation that topological characteristics of Gaussian fields depend on the power spectrum, as opposed to the geometric measures that are insensitive to the power spectrum characteristics.

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Topological data analysis and diagnostics of compressible magnetohydrodynamic turbulence

Cited by 6 publications

References 52 publications

Is the observable Universe consistent with the cosmological principle?

Is the observable Universe consistent with the cosmological principle?

Topology and geometry of Gaussian random fields I: on Betti numbers, Euler characteristic, and Minkowski functionals

Topology and geometry of Gaussian random fields II: on critical points, excursion sets, and persistent homology

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