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J. Phys. Soc. Jpn. 80 (2011) 074003 (5 pages)  |Previous Article| |Next Article|  |Table of Contents|
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Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background

Naoki Kobayashi, Yoshihiro Yamazaki1, Hiroto Kuninaka2, Makoto Katori, Mitsugu Matsushita, Satoki Matsushita3, and Lung-Yih Chiang3

Department of Physics, Chuo University, Bunkyo, Tokyo 112-8551, Japan
1Department of Physics, Waseda University, Shinjuku, Tokyo 169-8555, Japan
2Faculty of Education, Mie University, Tsu 514-8507, Japan
3Institute of Astronomy and Astrophysics, Academia Sinica, Taipei 10617, R.O.C.

(Received December 8, 2010; Accepted April 4, 2011; Published June 27, 2011)

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 ζ 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 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 He≃0.23 < 1/2. ©2011 The Physical Society of Japan

URL: http://jpsj.ipap.jp/link?JPSJ/80/074003/
DOI: 10.1143/JPSJ.80.074003


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