The sponge-like topology of large-scale structure in the universe

Gott, J. Richard; Dickinson, M.; Melott, Adrian L.

doi:10.1086/164347

Cited by 344 publications

(339 citation statements)

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“…Since we have numerous studies that show that the threedimensional topology of large-scale structure is spongelike (Gott et al 1986;Vogeley et al 1994;Hikage et al 2002), it should not be surprising that as we look at larger samples we should find examples of larger connected structures. Indeed, we would have had to have been especially lucky to have discovered the largest structure in the observable universe in the initial CfA survey, which has a much smaller volume than the Sloan survey.…”

Section: Now the Product Of Two Complex Numbersmentioning

confidence: 99%

A Map of the Universe

Gott

Jurić

Schlegel

et al. 2005

ApJ

321

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We have produced a new conformal map of the universe illustrating recent discoveries, ranging from Kuiper Belt objects in the solar system to the galaxies and quasars from the Sloan Digital Sky Survey. This map projection, based on the logarithm map of the complex plane, preserves shapes locally and yet is able to display the entire range of astronomical scales from the Earth's neighborhood to the cosmic microwave background. The conformal nature of the projection, preserving shapes locally, may be of particular use for analyzing large-scale structure. Prominent in the map is a Sloan Great Wall of galaxies 1.37 billion light-years long, 80% longer than the Great Wall discovered by Geller and Huchra and therefore the largest observed structure in the universe. Subject heading gs: large-scale structure of universe -methods: data analysis

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Section: Now the Product Of Two Complex Numbersmentioning

confidence: 99%

A Map of the Universe

Gott

Jurić

Schlegel

et al. 2005

ApJ

321

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“…Perhaps the most natural way to proceed and characterize non-Gaussian statistical signatures is by using higher-order poly-spectra [1], or equivalently, three-point and higher-order correlation functions [2][3][4][5][6][7][8][9][10]. 1 An interesting, and less explored alternative, originally suggested in the context of the cosmic density field [12], is to utilize topological features.…”

Section: Introductionmentioning

confidence: 99%

Probing cosmology with weak lensing Minkowski functionals

et al. 2012

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In this paper, we show that Minkowski Functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we run a large suite of cosmological ray-tracing N-body simulations to create mock weak WL convergence maps, and study the cosmological information content of MFs derived from these maps. Our suite consists of 80 independent 512 3 N-body runs, covering seven different cosmologies, varying three cosmological parameters Ωm, w, and σ8 one at a time, around a fiducial ΛCDM model. In each cosmology, we use ray-tracing to create a thousand pseudo-independent 12 deg 2 convergence maps, and use these in a Monte Carlo procedure to estimate the joint confidence contours on the above three parameters. We include redshift tomography at three different source redshifts zs = 1, 1.5, 2, explore five different smoothing scales θG = 1, 2, 3, 5, 10 arcmin, and explicitly compare and combine the MFs with the WL power spectrum. We find that the MFs capture a substantial amount of information from non-Gaussian features of convergence maps, i.e. beyond the power spectrum. The MFs are particularly well suited to break degeneracies and to constrain the dark energy equation of state parameter w (by a factor of ≈ three better than from the power spectrum alone). The non-Gaussian information derives partly from the one-point function of the convergence (through V0, the "area" MF), and partly through non-linear spatial information (through combining different smoothing scales for V0, and through V1 and V2, the boundary length and genus MFs, respectively). In contrast to the power spectrum, the best constraints from the MFs are obtained only when multiple smoothing scales are combined.

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“…Rather recently, more complex statistics of smoothed cosmic fields have become popular in cosmology, such as the genus statistic (Gott, Melott, & Dickinson 1986), density peak statistics (Bardeen et al 1986), area, length, and level-crossing statistics (Ryden 1988a), Minkowski functionals (Schmalzing & Buchert 1997), etc. These statistics provide assuring characterizations of the clustering pattern that cannot be perceived only by the hierarchy of cumulants or by the PDF.…”

Section: Introductionmentioning

confidence: 99%

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second‐Order Perturbation Theory

Matsubara¹

2003

ApJ

133

166

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We formulate a general method for perturbative evaluations of statistics of smoothed cosmic fields and provide useful formulae for application of the perturbation theory to various statistics. This formalism is an extensive generalization of the method used by Matsubara, who derived a weakly nonlinear formula of the genus statistic in a three-dimensional density field. After describing the general method, we apply the formalism to a series of statistics, including genus statistics, level-crossing statistics, Minkowski functionals, and a density extrema statistic, regardless of the dimensions in which each statistic is defined. The relation between the Minkowski functionals and other geometrical statistics is clarified. These statistics can be applied to several cosmic fields, including three-dimensional density field, three-dimensional velocity field, twodimensional projected density field, and so forth. The results are detailed for second-order theory of the formalism. The effect of the bias is discussed. The statistics of smoothed cosmic fields as functions of rescaled threshold by volume fraction are discussed in the framework of second-order perturbation theory. In CDMlike models, their functional deviations from linear predictions plotted against the rescaled threshold are generally much smaller than that plotted against the direct threshold. There is still a slight meatball shift against rescaled threshold, which is characterized by asymmetry in depths of troughs in the genus curve. A theory-motivated asymmetry factor in the genus curve is proposed.

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The sponge-like topology of large-scale structure in the universe

Cited by 344 publications

References 5 publications

A Map of the Universe

A Map of the Universe

Probing cosmology with weak lensing Minkowski functionals

Statistics of Smoothed Cosmic Fields in Perturbation Theory. I. Formulation and Useful Formulae in Second‐Order Perturbation Theory

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