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Abstract

Fractal Geometry of One-dimensional Cosmological Models with Scale-Free Initial Conditions

Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so, over what range of scales. One dimensional models demonstrate that the important dynamics for cluster formation occurs in the position-velocity plane. Here we investigate the development of scaling behavior and multifractal geometry for a family of one dimensional models for three different, scale-free, initial conditions. Under special circumstances we confirm a simple relation between the power spectrum, correlation function, and correlation dimension.

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