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On the Fractal Dimension of the Visible Universe

Jean-Pierre Eckmann·Esa Järvenpää·Maarit Järvenpää·Itamar Procaccia
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Abstract

Estimates of the fractal dimension $D$ of the set of galaxies in the universe, based on ever improving data sets, tend to settle on $D\approx 2$. This result raised a raging debate due to its glaring contradiction with astrophysical models that expect a homogeneous universe. A recent mathematical result indicates that there is no contradiction, since measurements of the dimension of the {\em visible} subset of galaxies is bounded from above by D=2 even if the true dimension is anything between D=2 and D=3. We demonstrate this result in the context of a simple fractal model, and explain how to proceed in order to find a better estimate of the true dimension of the set of galaxies.

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Jean-Pierre Eckmann, Esa Järvenpää, Maarit Järvenpää, Itamar Procaccia. 2003-01-03. On the Fractal Dimension of the Visible Universe. https://arxiv.org/abs/astro-ph/0301034

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