Cosmological Perturbation Theory and the Spherical Collapse Model - II. Non-Gaussian initial conditions

Abstract

In Part I of this series, we introduced the Spherical Collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants ${\xi }_J$ of density fluctuations in cosmological Perturbation Theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic Non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the $J$-point functions. We argue that for the hierarchical ratios $S_J$, these non-local terms are sub-dominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results to Non-Gaussian N-body simulations, which turn out to be in very good agreement up to scales where $σ\simlt 1$.

12 pages, Latex, 8 figures. New section with predictions for the Isocurvature CDM cosmogony added. Accepted for publication in MNRAS

Cited by in corpus (26)

• How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering
• Large-scale structure, the cosmic microwave background, and primordial non-gaussianity
• Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
• Noninteracting dark matter
• The 2dF Galaxy Redshift Survey: higher order galaxy correlation functions
• An analytic model for the bispectrum of galaxies in redshift space
• Biased-estimations of the Variance and Skewness
• The 2dF Galaxy Redshift Survey: Hierarchical galaxy clustering
• Non-Linear gravitational growth of large scale structures inside and outside standard Cosmology
• Reconstruction of primordial density fields
• Primordial non-Gaussianity in the large scale structure of the Universe
• Primordial non-Gaussianity without tails -- how to measure fNL with the bulk of the density PDF
• On the trispectrum as a gaussian test for cosmology
• The Hunt for Primordial Interactions in the Large Scale Structures of the Universe
• Gravitational Evolution of the Large-Scale Probability Density Distribution: The Edgeworth & Gamma Expansions
• Gravitational Clustering from Chi^2 Initial Conditions
• Hunting high and low: Disentangling primordial and late-time non-Gaussianity with cosmic densities in spheres
• Skewness as a probe of non-Gaussian initial conditions
• Predictions for the clustering properties of the Lyman-alpha Forest - I. One-point statistics
• Higher order moments of the density field in a parameterized sequence of non-gaussian theories
• A New Angle on Gravitational Clustering
• Constraints on shear and rotation with massive galaxy clusters
• The VIMOS Public Extragalactic Redshift Survey (VIPERS). Hierarchical scaling and biasing
• The Real and Redshift Space Density Distribution Function for Large-Scale Structure in the Spherical Collapse Approximation
• 2-Point Moments in Cosmological Large Scale Structure: I. Theory and Comparison with Simulations
• High-order 2MASS galaxy correlation functions: Probing the primordial density field and the linearity of galaxy bias