### 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 De of the entire pattern of isothermal lines, the fractal dimension Dc of a single isothermal line, the exponent ε in Korčak's law for the size distribution of isothermal loops, the two kind of Hurst exponents, He for the profile of the CMB radiation temperature, and Hc 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 A cold dark matter (ACDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the ACDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by He = 0.23 < 1=2.

Original language | English |
---|---|

Article number | 074003 |

Journal | Journal of the Physical Society of Japan |

Volume | 80 |

Issue number | 7 |

DOIs | |

Publication status | Published - 2011 Jul |

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### Keywords

- Cosmic microwave background radiation
- Fractal analysis
- Hurst exponent
- Isothermal lines and loops
- Self-affinity

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of the Physical Society of Japan*,

*80*(7), [074003]. https://doi.org/10.1143/JPSJ.80.074003

**Fractal structure of isothermal lines and loops on the cosmic microwave background.** / Kobayashi, Naoki; Yamazaki, Yoshihiro; Kuninaka, Hiroto; Katori, Makoto; Matsushita, Mitsugu; Matsushita, Satoki; Chiang, Lung Yih.

Research output: Contribution to journal › Article

*Journal of the Physical Society of Japan*, vol. 80, no. 7, 074003. https://doi.org/10.1143/JPSJ.80.074003

}

TY - JOUR

T1 - Fractal structure of isothermal lines and loops on the cosmic microwave background

AU - Kobayashi, Naoki

AU - Yamazaki, Yoshihiro

AU - Kuninaka, Hiroto

AU - Katori, Makoto

AU - Matsushita, Mitsugu

AU - Matsushita, Satoki

AU - Chiang, Lung Yih

PY - 2011/7

Y1 - 2011/7

N2 - 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 De of the entire pattern of isothermal lines, the fractal dimension Dc of a single isothermal line, the exponent ε in Korčak's law for the size distribution of isothermal loops, the two kind of Hurst exponents, He for the profile of the CMB radiation temperature, and Hc 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 A cold dark matter (ACDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the ACDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by He = 0.23 < 1=2.

AB - 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 De of the entire pattern of isothermal lines, the fractal dimension Dc of a single isothermal line, the exponent ε in Korčak's law for the size distribution of isothermal loops, the two kind of Hurst exponents, He for the profile of the CMB radiation temperature, and Hc 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 A cold dark matter (ACDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the ACDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by He = 0.23 < 1=2.

KW - Cosmic microwave background radiation

KW - Fractal analysis

KW - Hurst exponent

KW - Isothermal lines and loops

KW - Self-affinity

UR - http://www.scopus.com/inward/record.url?scp=79960411444&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960411444&partnerID=8YFLogxK

U2 - 10.1143/JPSJ.80.074003

DO - 10.1143/JPSJ.80.074003

M3 - Article

VL - 80

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 7

M1 - 074003

ER -