宇宙微波背景等温线和等温环的分形结构
Fractal Structure of Isothermal Lines and Loops on the Cosmic Microwave Background
摘要：
研究了宇宙微波背景（CMB）辐射在星图上的等温线和等温环的统计规律，证实了辐射温度起伏的分形结构。我们估计了等温线的分形维数$D_{\mathrm{e}}$、单条等温线的分形维数$D_{\mathrm{c}}$、Korčak定律中等温环尺寸分布的分形维数$ζ$、CMB辐射温度分布的分形维数$H_{\mathrm{e}}$和单条等温线的分形维数$H_{\mathrm{c}}$.我们还进行分形分析的两个人工天空图模拟的标准模型在物理宇宙学，WMAP最佳拟合$Λ$冷暗物质（$Λ$ CDM）模型，并通过高斯自由模型的粗糙表面。真实CMB辐射的温度波动和在使用$Λ$ CDM模型的模拟中是非高斯的，在这个意义上，等温线和环路的位移具有由$H_{\mathrm{e}} \simeq 0.23 < 1/2$表示的反持久性。
英文摘要：
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 $ζ$ in Korčak'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 $Λ$ Cold Dark Matter ($Λ$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 $Λ$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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