Excursion Set Theory for generic moving barriers and non-Gaussian initial conditions

Abstract

Excursion set theory, where density perturbations evolve stochastically with the smoothing scale, provides a method for computing the mass function of cosmological structures like dark matter halos, sheets and filaments. The computation of these mass functions is mapped into the so-called first-passage time problem in the presence of a moving barrier. In this paper we use the path integral formulation of the excursion set theory developed recently to analytically solve the first-passage time problem in the presence of a generic moving barrier, in particular the barrier corresponding to ellipsoidal collapse. We perform the computation for both Gaussian and non-Gaussian initial conditions. The expression of the halo mass function for the ellipsoidal collapse barrier and with non-Gaussianity is therefore obtained in a fully consistent way and it does not require the introduction of any form factor artificially derived from the Press-Schechter formalism based on the spherical collapse and usually adopted in the literature.

17 pages, 7 figures. Minor corrections to match the version published in MNRAS

References in corpus (30)

• Simulating the joint evolution of quasars, galaxies and their large-scale distribution
• Non-Gaussian features of primordial fluctuations in single field inflationary models
• Large scale bias and the peak background split
• Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes
• Mass function of dark matter halos
• Non-Gaussianity from Inflation: Theory and Observations
• An excursion set model of hierarchical clustering: Ellipsoidal collapse and the moving barrier
• The imprints of primordial non-gaussianities on large-scale structure: scale dependent bias and abundance of virialized objects
• The Growth of HII Regions During Reionization
• Constraints on local primordial non-Gaussianity from large scale structure
• The effect of primordial non-Gaussianity on halo bias
• The abundance of high-redshift objects as a probe of non-Gaussian initial conditions
• Effects of Scale-Dependent Non-Gaussianity on Cosmological Structures
• The Excursion Set Theory of Halo Mass Functions, Halo Clustering, and Halo Growth
• Primordial non-gaussianity, statistics of collapsed objects, and the Integrated Sachs-Wolfe effect
• Large-scale non-Gaussian mass function and halo bias: tests on N-body simulations
• Non-Gaussian halo bias and future galaxy surveys
• An excursion set model for the distribution of dark matter and dark matter haloes
• Structure formation from non-Gaussian initial conditions: multivariate biasing, statistics, and comparison with N-body simulations
• The Cosmological Mass Distribution Function in the Zel'dovich Approximation
• Detectability of the effect of Inflationary non-Gaussianity on halo bias
• The Halo Mass Function from Excursion Set Theory. II. The Diffusing Barrier
• An excursion set model of the cosmic web: The abundance of sheets, filaments and halos
• The Halo Mass Function from Excursion Set Theory. III. Non-Gaussian Fluctuations
• N-body simulations with generic non-Gaussian initial conditions I: Power Spectrum and halo mass function
• Constraining Primordial Non-Gaussianity With the Abundance of High Redshift Clusters
• Constraints on a non-gaussian (${\chi }_m^2$) CDM model
• Evolution of the cluster abundance in non-Gaussian models
• On Random Walks with a General Moving Barrier
• Halo abundances in the f_{nl} model

Cited by in corpus (34)

• Formation of Galaxy Clusters
• Large-Scale Galaxy Bias
• Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity
• Non-Gaussian Halo Bias Re-examined: Mass-dependent Amplitude from the Peak-Background Split and Thresholding
• Spherical collapse and halo mass function in f(R) theories
• The Non-Gaussian Halo Mass Function with fNL, gNL and tauNL
• Toward a Universal Formulation of the Halo Mass Function
• Halo abundances and counts-in-cells: The excursion set approach with correlated steps
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Halo clustering and g_{NL}-type primordial non-Gaussianity
• Excursion Set Halo Mass Function and Bias in a Stochastic Barrier Model of Ellipsoidal Collapse
• A high precision semi-analytic mass function
• The importance of stepping up in the excursion set approach
• Conditional Probabilities in the Excursion Set Theory. Generic Barriers and non-Gaussian Initial Conditions
• The Halo Void (Dust) Model of Large Scale Structure
• Statistics of Dark Matter Halos from the Excursion Set Approach
• The universal multiplicity function: counting halos and voids
• The Effect of Local non-Gaussianity on the Matter Bispectrum at Small Scales
• Primordial Non-Gaussianity and Reionization
• Non-Gaussianity and Excursion Set Theory: Halo Bias
• Non-Gaussian Halo Mass Function and Non-Spherical Halo Collapse: Theory vs. Simulations
• Modelling the shapes of the largest gravitationally bound objects
• Testing Multi-Field Inflation with Galaxy Bias
• Halo statistics in non-Gaussian cosmologies: the collapsed fraction, conditional mass function, and halo bias from the path-integral excursion set method
• A Consistent Comparison of Bias Models using Observational Data
• Peaks and dips in Gaussian random fields: a new algorithm for the shear eigenvalues, and the excursion set theory
• Scale-dependent bias from the primordial non-Gaussianity with a Gaussian-squared field
• Modification of the halo mass function by kurtosis associated with primordial non-Gaussianity
• Got plenty of nothing: cosmic voids as a probe of particle dark matter
• Fingerprints of Anomalous Primordial Universe on the Abundance of Large Scale Structures
• Higher moments of primordial non-Gaussianity and N-body simulations
• Comparison of the linear bias models in the light of the Dark Energy Survey
• The Extended Zel'dovich Mass Functions of Clusters and Isolated Clusters in the Presence of Primordial Non-Gaussianity
• A Hamiltonian Approach to Floating Barrier Option Pricing