Scale Dependent Dimension of Luminous Matter in the Universe

Abstract

We present a geometrical model of the distribution of luminous matter in the universe, derived from a very simple reaction-diffusion model of turbulent phenomena. The apparent dimension of luminous matter, $D(l)$, depends linearly on the logarithm of the scale $l$ under which the universe is viewed: $D(l)\sim 3\log (l/l_0)/\log (\xi /l_0)$, where $\xi$ is a correlation length. Comparison with data from the SARS red-shift catalogue, and the LEDA database provides a good fit with a correlation length $\xi \sim 300$ Mpc. The geometrical interpretation is clear: At small distances, the universe is zero-dimensional and point-like. At distances of the order of 1 Mpc the dimension is unity, indicating a filamentary, string-like structure; when viewed at larger scales it gradually becomes 2-dimensional wall-like, and finally, at and beyond the correlation length, it becomes uniform.

6 pages, 2 figures

References in corpus (5)

• Scale-invariance of galaxy clustering
• The Large-Scale Smoothness of the Universe
• The fractal distribution of galaxies and the transition to homogeneity
• Biasing in Gaussian random fields and galaxy correlations
• Scale Dependent Dimension in the Forest Fire Model

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• Random walk through fractal environments
• Scaling of voids and fractality in the galaxy distribution
• Cluster formation in complex multi-scale systems
• Familon Model of Dark Matter
• Log-Poisson Statistics and Extended Self-Similarity in Driven Dissipative Systems