Statistical Cosmology with Quadratic Density Fields

Abstract

Primordial fluctuations in the cosmic density are usually assumed to take the form of a Gaussian random field that evolves under the action of gravitational instability. In the early stages, while they have low amplitude, the fluctuations grow linearly. During this phase the Gaussian character of the fluctuations is preserved. Later on, when the fluctuations have amplitude of order the mean density or larger, non-linear effects cause departures from Gaussianity. In Fourier space, non-linearity is responsible for coupling Fourier modes and altering the initially random distribution of phases that characterizes Gaussian initial conditions. In this paper we investigate some of the effects of quadratic non-linearity on basic statistical properties of cosmological fluctuations. We demonstrate how this form of non-linearity can affect asymptotic properties of density fields such as homogeneity, ergodicity, and behaviour under smoothing. We also show how quadratic density fluctuations give rise to a particular relationship between the phases of different Fourier modes which, in turn, leads to the generation of a non-vanishing bispectrum. We thus elucidate the relationship between higher-order power spectra and phase distributions.

Submitted to MNRAS

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• Genus Topology of the Cosmic Microwave Background from the WMAP 3-Year Data
• Phase Correlations in Non-Gaussian Fields
• Fourier Phase Analysis of SDSS Galaxies
• Statistics of Fourier Modes in Non-Gaussian Fields
• The Distribution Function of the Phase Sum as a Signature of Phase Correlations Induced by Nonlinear Gravitational Clustering
• Auto and cross correlation of phases of the whole-sky CMB and foreground maps from the 1-year WMAP data
• Scale Transformations, Tree-level Perturbation Theory, and the Cosmological Matter Bispectrum
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• Minkowski Tensors in Redshift Space -- Beyond the Plane Parallel Approximation
• An Introduction into the Theory of Cosmological Structure Formation
• Non-perturbative $\delta N$
• The relation between the two-point and the three-point correlation functions in the non-linear gravitational clustering regime
• Spawning and merging of Fourier modes and phase coupling in cosmological density bispectrum
• Dark matter vorticity and velocity dispersion from truncated Dyson$\unicode{x2013}$Schwinger equations
• Phase statistics of the WMAP 7 year data
• Cosmological functional renormalisation group, extended Galilean invariance and the sweeping effect
• Note on Redshift Distortion in Fourier Space