arXiv 2007.018122020-07-03astro-ph.CO

阶段IV光谱测量的Fisher方法验证

Validating the Fisher approach for stage IV spectroscopic surveys

S. Yahia-Cherif, A. Blanchard, S. Camera, S. Ilić, K. Markovič, A. Pourtsidou, Z. Sakr, D. Sapone, I. Tutusaus

备注：: 20 pages, 10 figures, 11 tables
发表信息：: A&A 649, A52 (2021)
DOI：: 10.1051/0004-6361/201937312

摘要：

近年来，预测活动已成为设计和优化大尺度结构测量的一个非常重要的工具。为了预测这样的调查的表现，费舍尔矩阵形式主义经常被用作计算宇宙学参数约束的快速和简单的方法。其中之一就是对暗能量性质的研究，这是现代宇宙学的主要目标之一。因此，品质因数（FoM）提供了一个测量约束暗能量的功率的度量。这被定义为由Chevallier-Polarski-Linder参数化中的暗能量状态方程参数$\{w_0,w_a\}$的联合方差给出的表面轮廓的逆，其可以从参数的协方差矩阵进行评估。该协方差矩阵是Fisher矩阵的逆矩阵。如果Fisher矩阵的元素估计精度不足，则病态矩阵的反演会导致协方差系数上的大误差。条件数是一种度量，为可靠的反演提供所需精度的数学下限，但在实践中，对于大小大于$2\times2$的Fisher矩阵，条件数往往过于严格。在本文中，我们提出了一个通用的数值方法，以保证一定的精度推断的约束，如FoM。它包括随机振动（扰动）的Fisher矩阵元素与高斯扰动的给定幅度，然后评估的最大幅度，保持FoM在选定的精度。然后，可以相应地选择用于计算Fisher矩阵元素的数值导数和积分中的步骤，以保持Fisher矩阵元素的精度低于此最大幅度。

英文摘要：

In recent years forecasting activities have become a very important tool for designing and optimising large scale structure surveys. To predict the performance of such surveys, the Fisher matrix formalism is frequently used as a fast and easy way to compute constraints on cosmological parameters. Among them lies the study of the properties of dark energy which is one of the main goals in modern cosmology. As so, a metric for the power of a survey to constrain dark energy is provided by the Figure of merit (FoM). This is defined as the inverse of the surface contour given by the joint variance of the dark energy equation of state parameters $\{w_0,w_a\}$ in the Chevallier-Polarski-Linder parameterisation, which can be evaluated from the covariance matrix of the parameters. This covariance matrix is obtained as the inverse of the Fisher matrix. Inversion of an ill-conditioned matrix can result in large errors on the covariance coefficients if the elements of the Fisher matrix have been estimated with insufficient precision. The conditioning number is a metric providing a mathematical lower limit to the required precision for a reliable inversion, but it is often too stringent in practice for Fisher matrices with size larger than $2\times2$. In this paper we propose a general numerical method to guarantee a certain precision on the inferred constraints, like the FoM. It consists on randomly vibrating (perturbing) the Fisher matrix elements with Gaussian perturbations of a given amplitude, and then evaluating the maximum amplitude that keeps the FoM within the chosen precision. The steps used in the numerical derivatives and integrals involved in the calculation of the Fisher matrix elements can then be chosen accordingly in order to keep the precision of the Fisher matrix elements below this maximum amplitude...

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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英文摘要：

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