Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background

2010/12/31 by Naoki Kobayashi, Yoshihiro Yamazaki, Hiroto Kuninaka +5 · 13 citations
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Astrophysics #CMB cold spot #Cosmic background radiation #Cosmic microwave background #Cosmology and Gravitation Theories #Exponent #Fractal #Fractal dimension #Isothermal process #Mathematical analysis #Optics #Physics #Scientific Research and Discoveries #Statistical physics #Thermodynamics #Tsallis statistics #astro-ph.CO #cond-mat.stat-mech

paper · pdf · doi:10.1143/jpsj.80.074003

published in Journal of the Physical Society of Japan 80(7), 074003 (Physical Society of Japan) · JPSJ3, 5 pages, 4 figures, 1 table. v3: minor corrections made for publication in J. Phys. Soc. Jpn

openalex publication_date 2011/06/27 · arxiv created 2011/06/30 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The statistics of isothermal lines and loops of the Cosmic Microwave Background (CMB) radiation on the sky map is studied and the fractal structure is confirmed in the radiation temperature fluctuation. We estimate the fractal exponents, such as the fractal dimension D_e of the entire pattern of isothermal lines, the fractal dimension D_c of a single isothermal line, the exponent ζ in Kor\vcak's law for the size distribution of isothermal loops, the two kind of Hurst exponents, H_e for the profile of the CMB radiation temperature, and H_c for a single isothermal line. We also perform fractal analysis of two artificial sky maps simulated by a standard model in physical cosmology, the WMAP best-fit Λ Cold Dark Matter (ΛCDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the ΛCDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by H_e ≃ 0.23 < 1/2.

Citations

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