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

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

2010-12-08

arxiv.org/abs/1012.1701v3

J. Phys. Soc. Jpn. 80 (2011) 074003

Astronomy and Astrophysics

Astrophysics

Cosmology and Extragalactic Astrophysics

JPSJ3, 5 pages, 4 figures, 1 table. v3: minor corrections made for publication in J. Phys. Soc. Jpn

Scientific paper

10.1143/JPSJ.80.074003

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 $D_{\mathrm{e}}$ of the entire pattern of isothermal lines, the fractal dimension $D_{\mathrm{c}}$ of a single isothermal line, the exponent $\zeta$ in Kor\v{c}ak's law for the size distribution of isothermal loops, the two kind of Hurst exponents, $H_{\mathrm{e}}$ for the profile of the CMB radiation temperature, and $H_{\mathrm{c}}$ 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 $\Lambda$ Cold Dark Matter ($\Lambda$CDM) model, and by the Gaussian free model of rough surfaces. The temperature fluctuations of the real CMB radiation and in the simulation using the $\Lambda$CDM model are non-Gaussian, in the sense that the displacement of isothermal lines and loops has an antipersistent property indicated by $H_{\mathrm{e}} \simeq 0.23 < 1/2$.

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