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<p>We have recently argued that the expansion of the Universe is compatible not only with standard homogeneity, but also with fractal homogeneity in a hierarchical fractal cosmology. In this work we further test this paradigm using the galactic distances obtained from the Updated CfA Redshift Catalogs. We confirm that the observed multifractal spectrum is consistent with the weighted Cantor set models characteristic of turbulence in space magnetized plasmas such as the solar wind in heliosphere, the very local interstellar medium and even in laboratory experiments. The degree of multifractality is smaller than that found inside the heliosphere and shows some variations between nearby and more distant galaxies, which may be related to the presence of voids in the large-scale matter distribution. A possible asymmetry in the spectrum may be attributed to some deviations from the Hubble’s law for an ideal uniform expansion. Overall, the deviations from homogeneity revealed by multifractal analysis should be broadly consistent with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Lambda\)</EquationSource> </InlineEquation>CDM large-scale structure formation.</p>

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Fractal nature of galaxy clustering in the updated CfA redshift catalog

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  • 发表日期：

    2026年1月25日

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  • Wiesław M. Macek,
  • Dariusz Wójcik

摘要

We have recently argued that the expansion of the Universe is compatible not only with standard homogeneity, but also with fractal homogeneity in a hierarchical fractal cosmology. In this work we further test this paradigm using the galactic distances obtained from the Updated CfA Redshift Catalogs. We confirm that the observed multifractal spectrum is consistent with the weighted Cantor set models characteristic of turbulence in space magnetized plasmas such as the solar wind in heliosphere, the very local interstellar medium and even in laboratory experiments. The degree of multifractality is smaller than that found inside the heliosphere and shows some variations between nearby and more distant galaxies, which may be related to the presence of voids in the large-scale matter distribution. A possible asymmetry in the spectrum may be attributed to some deviations from the Hubble’s law for an ideal uniform expansion. Overall, the deviations from homogeneity revealed by multifractal analysis should be broadly consistent with \(\Lambda\) CDM large-scale structure formation.