A Study of High-Order Non-Gaussianity with Applications to Massive Clusters and Large Voids

Abstract

The statistical meaning of the local non-Gaussianity parameters f_NL and g_NL is examined in detail. Their relations to the skewness and the kurtosis of the probability distribution of density fluctuations are shown to obey simple fitting formulae, accurate on galaxy-cluster scales. We argue that the knowledge of f_NL and g_NL is insufficient for reconstructing a well-defined distribution of density fluctuations. However, by weakening the statistical significance of f_NL and g_NL, it is possible to reconstruct a well-defined pdf by using a truncated Edgeworth series. We give some general guidelines on the use of such a series, noting in particular that 1) the Edgeworth series cannot represent models with nonzero f_NL, unless g_NL is nonzero also, 2) the series cannot represent models with g_NL<0, unless some higher-order non-Gaussianities are known. Finally, we apply the Edgeworth series to calculate the effects of g_NL on the abundances of massive clusters and large voids. We show that the abundance of voids may generally be more sensitive to high-order non-Gaussianities than the cluster abundance.

14 pages, lots of interesting figures. This version supersedes the ApJ version. Fitting formulae corrected

References in corpus (34)

• Baryonic Features in the Matter Transfer Function
• An analytic model for the spatial clustering of dark matter haloes
• Non-Gaussianity from Inflation: Theory and Observations
• DBI in the Sky
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Primordial Non-Gaussianities from Inflation Models
• Ghost Inflation
• Non-Gaussianity of the primordial perturbation in the curvaton model
• The effect of primordial non-Gaussianity on halo bias
• Expansions for nearly Gaussian distributions
• On Non-Gaussianity in the Curvaton Scenario
• Running Non-Gaussianities in DBI Inflation
• The Aspen--Amsterdam Void Finder Comparison Project
• Scale-dependent bias induced by local non-Gaussianity: A comparison to N-body simulations
• Review of local non-Gaussianity from multi-field inflation
• Primordial fluctuations and non-Gaussianities in multi-field DBI inflation
• Large-scale non-Gaussian mass function and halo bias: tests on N-body simulations
• Large non-Gaussianity in multiple-field inflation
• Constraining Running Non-Gaussianity
• Properties of the Cosmological Density Distribution Function
• Weakly Non-Linear Gaussian Fluctuations and the Edgeworth Expansion
• The Halo Mass Function from Excursion Set Theory. II. The Diffusing Barrier
• Signature of primordial non-Gaussianity of phi^3-type in the mass function and bias of dark matter haloes
• Voids as a Precision Probe of Dark Energy
• Shapes and Sizes of Voids in the LCDM Universe: Excursion Set Approach
• On Minimally-Parametric Primordial Power Spectrum Reconstruction and the Evidence for a Red Tilt
• Void Ellipticity Distribution as a Probe of Cosmology
• The Void Abundance with Non-Gaussian Primordial Perturbations
• Evolution of the cluster abundance in non-Gaussian models
• Scale-dependent bias from primordial non-Gaussianity in general relativity
• Constraints on f_nl and g_nl from the analysis of the N-pdf of the CMB large scale anisotropies
• The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances
• Self-Calibrated Cluster Counts as a Probe of Primordial Non-Gaussianity
• The dependence of cosmological parameters estimated from the microwave background on non-gaussianity

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• Cosmic Voids in Sloan Digital Sky Survey Data Release 7
• The Hierarchical Structure and Dynamics of Voids
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• The Non-Gaussian Halo Mass Function with fNL, gNL and tauNL
• Constraining primordial non-Gaussianity via a multitracer technique with surveys by Euclid and Square Kilometre Array
• Cluster-Void Degeneracy Breaking: Dark Energy, Planck and the Largest Cluster & Void
• High-redshift JWST Observations and Primordial Non-Gaussianity
• Moment transport equations for the primordial curvature perturbation
• Number Counts and Non-Gaussianity
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Halo clustering and g_{NL}-type primordial non-Gaussianity
• Cluster-void degeneracy breaking: Neutrino properties and dark energy
• Excursion Sets and Non-Gaussian Void Statistics
• Primordial Non-Gaussianity and Extreme-Value Statistics of Galaxy Clusters
• Estimating f_NL and g_NL from Massive High-Redshift Galaxy Clusters
• Quantifying the rareness of extreme galaxy clusters
• Extreme-Value Statistics of the Spin of Primordial Black Holes
• Cluster-Void Degeneracy Breaking: Modified Gravity in the Balance
• Dark Matter-Dark Energy Interaction and the Shape of Cosmic Voids
• On the Abundance of Extreme Voids
• Modification of the halo mass function by kurtosis associated with primordial non-Gaussianity
• The 21cm Power Spectrum and the Shapes of Non-Gaussianity
• Scale-dependent bias from the primordial non-Gaussianity with a Gaussian-squared field
• Scale Dependence of the Halo Bias in General Local-Type Non-Gaussian Models I: Analytical Predictions and Consistency Relations
• The pairwise velocity probability density function in models with local primordial non-Gaussianity
• Scale-dependent Bias from the Reconstruction of Non-Gaussian Distributions
• Constraints on Non-Gaussianity from Sunyaev--Zeldovich Cluster Surveys
• Effects of dark matter pressure on the ellipticity of cosmic voids
• Halo/Galaxy Bispectrum with Equilateral-type Primordial Trispectrum
• Constraining cosmological parameters using void statistics from the SDSS survey
• The Lyman-alpha Forest as a tool for disentangling non-Gaussianities