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arXiv 0908.1696astro-ph.CO
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来自三次原始扰动的非高斯统计性质：CMB映射模拟和亏格统计

Statistical nature of non-Gaussianity from cubic order primordial perturbations: CMB map simulations and genus statistic

Pravabati Chingangbam, Changbom Park

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18+1 pages
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摘要：

我们模拟CMB地图，包括非高斯性所产生的原始引力势的三阶扰动，其特征在于由非线性参数$g_{NL}$。该地图被用来研究所产生的非高斯温度波动的特性。我们测量的属，并调查它如何偏离高斯形状的函数$g_{NL}$和平滑尺度。我们发现非高斯亏格曲线与高斯亏格曲线的偏差具有反对称的正弦函数形状，这意味着$g_{NL}>0$的热点和冷点较多，而$g_{NL}<0$的热点和冷点较少。偏差随$g_{NL}$线性增加，并且随着平滑尺度的增加也表现出轻微的增加。我们进一步研究了来自属的其他统计量，即，热点的数量，冷点的数量，热点和冷点的组合数量和属曲线在平均温度波动的斜率。我们发现，这些可观携带签名的$g_{NL}$，显然不同于二次阶扰动，编码在参数$f_{NL}$。因此，它们不仅可以区分非高斯温度波动和高斯温度波动，而且可以区分$g_{NL}$和$f_{NL}$型非高斯性。

英文摘要：

We simulate CMB maps including non-Gaussianity arising from cubic order perturbations of the primordial gravitational potential, characterized by the non-linearity parameter $g_{NL}$. The maps are used to study the characteristic nature of the resulting non-Gaussian temperature fluctuations. We measure the genus and investigate how it deviates from Gaussian shape as a function of $g_{NL}$ and smoothing scale. We find that the deviation of the non-Gaussian genus curve from the Gaussian one has an antisymmetric, sine function like shape, implying more hot and more cold spots for $g_{NL}>0$ and less of both for $g_{NL}<0$. The deviation increases linearly with $g_{NL}$ and also exhibits mild increase as the smoothing scale increases. We further study other statistics derived from the genus, namely, the number of hot spots, the number of cold spots, combined number of hot and cold spots and the slope of the genus curve at mean temperature fluctuation. We find that these observables carry signatures of $g_{NL}$ that are clearly distinct from the quadratic order perturbations, encoded in the parameter $f_{NL}$. Hence they can be very useful tools for distinguishing not only between non-Gaussian temperature fluctuations and Gaussian ones but also between $g_{NL}$ and $f_{NL}$ type non-Gaussianities.

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