Large-scale bias in the Universe: bispectrum method
Large-scale bias in the Universe: bispectrum method
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DOI：
10.1093/mnras/290.4.651
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发表时间：
1997-06
影响因子：
4.8
通讯作者：
S. Matarrese;L. Verde;A. Heavens
中科院分区：
文献类型：
--
作者：
S. Matarrese;L. Verde;A. Heavens
宇宙可能接近临界密度的证据主要来自于对大尺度结构的动力学研究，临界密度是宇宙膨胀最终停止所必需的。这些研究要么直接利用观测到的星系特有的速度场，要么通过在红移巡天中量化其对星系成团的各向异性影响来间接地进行。这两种方法的潜在困难是，如果使用线性微扰理论，则仅在组合$\beta = \Omega_0^{0.6}/B$中获得密度参数$\Omega_0$。因此，密度参数$\Omega_0 $的确定受到了偏差参数$B$缺乏良好测量的影响，该参数将样本星系的聚集与质量的聚集联系起来。在本文中，我们发展了Fry（1994）的思想，利用二阶微扰理论研究如何在大尺度上测量偏置参数。高阶统计量的使用允许提升$B$和$\Omega_0$之间的简并性，然后明确地确定$\Omega_0$成为可能。我们采用似然方法的双谱，傅立叶空间中的三点函数。本文是第一步，把这个想法变成一个实际的命题红移调查，主要是关注的噪声特性的双谱，这是非平凡的。所需的双谱协方差的计算涉及六点函数，包括许多噪声项，为此，我们已经开发了一种生成函数的方法，这将是在计算高阶统计的价值一般。
Evidence that the Universe may be close to the critical density, required for its expansion eventually to be halted, comes principally from dynamical studies of large-scale structure. These studies either use the observed peculiar velocity field of galaxies directly, or indirectly by quantifying its anisotropic effect on galaxy clustering in redshift surveys. A potential difficulty with both such approaches is that the density parameter $\Omega_0$ is obtained only in the combination $\beta = \Omega_0^{0.6}/b$, if linear perturbation theory is used. The determination of the density parameter $\Omega_0$ is therefore compromised by the lack of a good measurement of the bias parameter $b$, which relates the clustering of sample galaxies to the clustering of mass. In this paper, we develop an idea of Fry (1994), using second-order perturbation theory to investigate how to measure the bias parameter on large scales. The use of higher-order statistics allows the degeneracy between $b$ and $\Omega_0$ to be lifted, and an unambiguous determination of $\Omega_0$ then becomes possible. We apply a likelihood approach to the bispectrum, the three-point function in Fourier space. This paper is the first step in turning the idea into a practical proposition for redshift surveys, and is principally concerned with noise properties of the bispectrum, which are non-trivial. The calculation of the required bispectrum covariances involves the six-point function, including many noise terms, for which we have developed a generating functional approach which will be of value in calculating high-order statistics in general.