# Real Space Statistical Properties of Standard Cosmological Models

Abstract : After reviewing some basic relevant properties of stationary stochastic processes (SSP), we discuss the properties of the so-called Harrison-Zeldovich like spectra of mass density perturbations. These correlations are a fundamental feature of all current standard cosmological models. Examining them in real space we note they imply a sub-poissonian normalized variance in spheres $\omega_M^2$(R) ~ $R^{-4} lnR$. In particular this latter behavior is at the limit of the most rapid decay (~ $R^{-4}$) of this quantity possible for any stochastic distribution (continuous or discrete). In a simple classification of all SSP into three categories, we highlight with the name "super-homogeneous'' the properties of the class to which models like this, with P(0) = 0, belong. In statistical physics language they are well described as lattice or glass-like. We illustrate their properties through two simple examples: (i) the "shuffled'' lattice and the One Component Plasma at thermal equilibrium.
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http://hal.in2p3.fr/in2p3-00192495
Contributor : Dominique Girod <>
Submitted on : Wednesday, November 28, 2007 - 1:02:17 PM
Last modification on : Monday, December 14, 2020 - 9:52:08 AM

### Citation

A. Gabrielli, M. Joyce, F. Sylos Labini. Real Space Statistical Properties of Standard Cosmological Models. 7th Granada Seminar of Computational and Statistical Physics, Sep 2002, Granada, Spain. pp.188-194, ⟨10.1063/1.1571311⟩. ⟨in2p3-00192495⟩

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