An Improved Calculation of the Non-Gaussian Halo Mass Function

Abstract

The abundance of collapsed objects in the universe, or halo mass function, is an important theoretical tool in studying the effects of primordially generated non-Gaussianities on the large scale structure. The non-Gaussian mass function has been calculated by several authors in different ways, typically by exploiting the smallness of certain parameters which naturally appear in the calculation, to set up a perturbative expansion. We improve upon the existing results for the mass function by combining path integral methods and saddle point techniques (which have been separately applied in previous approaches). Additionally, we carefully account for the various scale dependent combinations of small parameters which appear. Some of these combinations in fact become of order unity for large mass scales and at high redshifts, and must therefore be treated non-perturbatively. Our approach allows us to do this, and to also account for multi-scale density correlations which appear in the calculation. We thus derive an accurate expression for the mass function which is based on approximations that are valid over a larger range of mass scales and redshifts than those of other authors. By tracking the terms ignored in the analysis, we estimate theoretical errors for our result and also for the results of others. We also discuss the complications introduced by the choice of smoothing filter function, which we take to be a top-hat in real space, and which leads to the dominant errors in our expression. Finally, we present a detailed comparison between the various expressions for the mass functions, exploring the accuracy and range of validity of each.

28 pages, 13 figures; v2: text reorganized and some figured modified for clarity, results unchanged, references added. Matches version published in JCAP

References in corpus (9)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• Effects of Scale-Dependent Non-Gaussianity on Cosmological Structures
• Primordial non-Gaussianity from the large scale structure
• Structure formation from non-Gaussian initial conditions: multivariate biasing, statistics, and comparison with N-body simulations
• The Void Abundance with Non-Gaussian Primordial Perturbations
• Primordial non-Gaussianity from the covariance of galaxy cluster counts
• Cosmological Parameters Degeneracies and Non-Gaussian Halo Bias
• Implications for Primordial Non-Gaussianity (f_NL) from weak lensing masses of high-z galaxy clusters

Cited by in corpus (36)

• Observational Probes of Cosmic Acceleration
• Cosmological Parameters from Observations of Galaxy Clusters
• Cosmology and Fundamental Physics with the Euclid Satellite
• Primordial non-Gaussianity in the Bispectrum of the Halo Density Field
• Cosmology from the Thermal Sunyaev-Zel'dovich Power Spectrum: Primordial non-Gaussianity and Massive Neutrinos
• The Non-Gaussian Halo Mass Function with fNL, gNL and tauNL
• Constraints on Primordial Non-Gaussianity from Large Scale Structure Probes
• N-body simulations with generic non-Gaussian initial conditions II: Halo bias
• Implications of multiple high-redshift galaxy clusters
• Unveiling the Dynamics of the Universe
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Halo clustering and g_{NL}-type primordial non-Gaussianity
• Measuring the neutrino mass from future wide galaxy cluster catalogues
• The clustering of galaxies and galaxy clusters: constraints on primordial non-Gaussianity from future wide-field surveys
• Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse
• Hunting high and low: Disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres
• Estimating f_NL and g_NL from Massive High-Redshift Galaxy Clusters
• Probability of the most massive cluster under non-Gaussian initial conditions
• Relativistic effects and primordial non-Gaussianity in the galaxy bias
• Isocurvature Perturbations and Non-Gaussianity of Gravitationally Produced Nonthermal Dark Matter
• A critical analysis of high-redshift, massive galaxy clusters: I
• The Effect of Local non-Gaussianity on the Matter Bispectrum at Small Scales
• Taming assembly bias for primordial non-Gaussianity
• Non-Gaussianity and Excursion Set Theory: Halo Bias
• Primordial Non-Gaussianity and Reionization
• Non-Gaussian halo abundances in the excursion set approach with correlated steps
• Non-Gaussian Halo Mass Function and Non-Spherical Halo Collapse: Theory vs. Simulations
• Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method
• The Extreme Tail of the Non-Gaussian Mass Function
• Application of cross correlations between CMB and large scale structure to constraints on the primordial non-Gaussianity
• Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
• Fingerprints of Anomalous Primordial Universe on the Abundance of Large Scale Structures
• Modification of the halo mass function by kurtosis associated with primordial non-Gaussianity
• The effect of primordial non-Gaussianity on the skeleton of cosmic shear maps
• Higher moments of primordial non-Gaussianity and N-body simulations
• A revisited Correction to the Halo Mass Function for local-type Primordial non-Gaussianity