arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1908.02440astro-ph.CO
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红移空间中高斯随机场三维Minkowski张量的包络平均

Ensemble Average of Three-Dimensional Minkowski Tensors of a Gaussian Random Field in Redshift Space

Stephen Appleby, Joby P. K., Pravabati Chingangbam, Changbom Park

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摘要：

本文给出了线性红移空间畸变高斯随机场三维平移不变秩2 Minkowski张量的系综期望值。闵可夫斯基张量$W^{0,2}_{1}$、$W^{0,2}_{2}$对场中存在的全局各向异性信号敏感，并且通过从低红移物质密度中提取这些统计数据，可以对红移空间失真参数$β= f/b$施加约束。我们首先回顾计算的合奏期望值$\langle W^{0,2}_{1} \rangle$，$\langle W^{0,2}_{2} \rangle $各向同性，高斯随机场，然后考虑如何修改这些结果的存在下，线性各向异性信号。在假设所有场保持高斯分布的情况下，我们计算了在与视线一致的坐标系中由于红移空间畸变引起的各向异性校正，发现$\langle W^{0,2}_{1} \rangle $，$\langle W^{0,2}_{2} \rangle $的对角元素之间的不等式。这些矩阵的对角元素的比率提供了一组仅对红移空间失真参数$β$敏感的统计。我们估计了可以从Minkowski张量中提取的Fisher信息，发现$W^{0,2}_{1}$比$W^{0,2}_{2}$对$β$更敏感，并且精确到$\sim 1\%$的$W^{0,2}_{1}$的测量可以产生对$β$的$\sim 4\%$约束。最后，我们讨论了直接使用闵可夫斯基张量的矩阵元素与测量特征值之间的区别。为了宇宙学参数估计的目的，我们提倡使用矩阵元素，以避免由特征值分解产生的虚假各向异性信号。

英文摘要：

We present the ensemble expectation values for the translation invariant, rank-2 Minkowski tensors in three-dimensions, for a linearly redshift space distorted Gaussian random field. The Minkowski tensors $W^{0,2}_{1}$, $W^{0,2}_{2}$ are sensitive to global anisotropic signals present within a field, and by extracting these statistics from the low redshift matter density one can place constraints on the redshift space distortion parameter $β= f/b$. We begin by reviewing the calculation of the ensemble expectation values $\langle W^{0,2}_{1} \rangle$, $\langle W^{0,2}_{2} \rangle $ for isotropic, Gaussian random fields, then consider how these results are modified by the presence of a linearly anisotropic signal. Under the assumption that all fields remain Gaussian, we calculate the anisotropic correction due to redshift space distortion in a coordinate system aligned with the line of sight, finding inequality between the diagonal elements of $\langle W^{0,2}_{1} \rangle $, $\langle W^{0,2}_{2} \rangle $. The ratio of diagonal elements of these matrices provides a set of statistics that are sensitive only to the redshift space distortion parameter $β$. We estimate the Fisher information that can be extracted from the Minkowski tensors, and find $W^{0,2}_{1}$ is more sensitive to $β$ than $W^{0,2}_{2}$, and a measurement of $W^{0,2}_{1}$ accurate to $\sim 1\%$ can yield a $\sim 4\%$ constraint on $β$. Finally, we discuss the difference between using the matrix elements of the Minkowski tensors directly against measuring the eigenvalues. For the purposes of cosmological parameter estimation we advocate the use of the matrix elements, to avoid spurious anisotropic signals that can be generated by the eigenvalue decomposition.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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