超越凯泽红移-空间畸变公式：星系团效应及其可探测性的全面广义相对论说明
Going beyond the Kaiser redshift-space distortion formula: a full general relativistic account of the effects and their detectability in galaxy clustering
摘要：
凯泽红移-空间畸变公式在小尺度上很好地描述了红移巡天中的星系团，但在大尺度上会产生许多附加项。其中一些术语可以用牛顿动力学来描述，并在文献中进行了讨论，而其他术语则需要最近才开发的适当的广义相对论描述。在星系团中解释这些术语是在视界尺度上检验广义相对论的第一步。这些影响可以分为两个方面，代表速度和重力位的贡献。它们的振幅是由体积、光度、距离涨落效应、星系数密度和哈勃参数的时间演化等因素决定的。我们比较了在红移空间畸变文献中常用的牛顿近似和完全广义相对论方程，发现牛顿近似可以解释大部分的速度效应。我们进行了Fisher矩阵分析，这些条款的可检测性，并表明，在一个单一的示踪剂调查，他们是完全无法检测到的。为了检测这些条款，必须诉诸最近开发的方法，以减少采样方差和散粒噪声。我们发现，在低红移的全天星系红移巡天中，如果可以利用质量M>10^12 Msun的晕（在一些更乐观的情况下，这可以增加到10-sigma或更高），速度项可以在几个sigma处测量，而引力势项本身只能勉强检测到。我们还表明，广义相对论效应是不退化的原始非高斯签名在星系的偏见，和检测原始非高斯的能力是妥协。
英文摘要：
Kaiser redshift-space distortion formula describes well the clustering of galaxies in redshift surveys on small scales, but there are numerous additional terms that arise on large scales. Some of these terms can be described using Newtonian dynamics and have been discussed in the literature, while the others require proper general relativistic description that was only recently developed. Accounting for these terms in galaxy clustering is the first step toward tests of general relativity on horizon scales. The effects can be classified as two terms that represent the velocity and the gravitational potential contributions. Their amplitude is determined by effects such as the volume and luminosity distance fluctuation effects and the time evolution of galaxy number density and Hubble parameter. We compare the Newtonian approximation often used in the redshift-space distortion literature to the fully general relativistic equation, and show that Newtonian approximation accounts for most of the terms contributing to velocity effect. We perform a Fisher matrix analysis of detectability of these terms and show that in a single tracer survey they are completely undetectable. To detect these terms one must resort to the recently developed methods to reduce sampling variance and shot noise. We show that in an all-sky galaxy redshift survey at low redshift the velocity term can be measured at a few sigma if one can utilize halos of mass M>10^12 Msun (this can increase to 10-sigma or more in some more optimistic scenarios), while the gravitational potential term itself can only be marginally detected. We also demonstrate that the general relativistic effect is not degenerate with the primordial non-Gaussian signature in galaxy bias, and the ability to detect primordial non-Gaussianity is little compromised.
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