Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models

Abstract

The initial conditions describing seed fluctuations for the formation of structure in standard cosmological models, i.e.the Harrison-Zeldovich distribution, have very characteristic ``super-homogeneous'' properties: they are statistically translation invariant, isotropic, and the variance of the mass fluctuations in a region of volume V grows slower than V. We discuss the geometrical construction of distributions of points in ${\mathbf{R}}^3$ with similar properties encountered in tiling and in statistical physics, e.g. the Gibbs distribution of a one-component system of charged particles in a uniform background (OCP). Modifications of the OCP can produce equilibrium correlations of the kind assumed in the cosmological context. We then describe how such systems can be used for the generation of initial conditions in gravitational $N$-body simulations.

7 pages, 3 figures, final version with minor modifications, to appear in PRD

References in corpus (6)

• Evolution of structure in cold dark matter universes
• Cosmic Temperature Fluctuations from Two Years of COBE DMR Observations
• The Glass-like Universe: Real-space correlation properties of standard cosmological models
• Fundamental Discreteness Limitations of Cosmological N-Body Clustering Simulations
• Power-law correlation and discreteness in cosmological N-body simulations
• On the problem of initial conditions in cosmological N-body simulations

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