arXiv 1406.60952014-06-23astro-ph.COastro-ph.GA

星系巡天的信息量

The information content of galaxy surveys

Julien Carron

备注：: Phd Thesis ETH Zurich, September 2012. 162 p. http://dx.doi.org/10.3929/ethz-a-007606553

摘要：

本论文的主要内容是研究重尾随机场的信息量，特别是对数正态场，即物质密度涨落场的模型。众所周知，在结构形成的非线性区域中，物质涨落场发展出如此大的尾部。也有人认为，具有大尾部的场不一定能用$N$ -点函数的层次结构很好地描述。在这篇论文中，我们能够使这最后一句话精确和对数正态模型的帮助下，精确地量化其影响的宇宙学参数的推断：我们发现，作为我们的主要结果，只有一小部分的总费舍尔信息的字段仍然包含在层次结构的$N$ -点时刻的非线性制度，呈现参数推断从这样的时刻非常低效。我们表明，该层次结构未能捕捉到的信息，包含在undersense区域，这在同一时间被发现是最丰富的信息。我们进一步发现我们的结果是非常一致的数值分析使用$N$体模拟。我们还讨论了这些问题的帮助下，明确的家庭领域的$N$ -点时刻在这项工作中定义的相同层次结构。类似的分析，然后应用到收敛场，沿视线的物质密度波动场的加权投影，具有类似的结论。我们还展示了如何简单的映射可以纠正这种不足，与文献中以前的研究结果一致（摘要）。

英文摘要：

A large fraction of this thesis is dedicated to the study of the information content of random fields with heavy tails, in particular the lognormal field, a model for the matter density fluctuation field. It is well known that in the nonlinear regime of structure formation, the matter fluctuation field develops such large tails. It has also been suggested that fields with large tails are not necessarily well described by the hierarchy of $N$-point functions. In this thesis, we are able to make this last statement precise and with the help of the lognormal model to quantify precisely its implications for inference on cosmological parameters : we find as our main result that only a tiny fraction of the total Fisher information of the field is still contained in the hierarchy of $N$-point moments in the nonlinear regime, rendering parameter inference from such moments very inefficient. We show that the hierarchy fails to capture the information that is contained in the underdense regions, which at the same time are found to be the most rich in information. We find further our results to be very consistent with numerical analysis using $N$-body simulations. We also discuss these issues with the help of explicit families of fields with the same hierarchy of $N$-point moments defined in this work. A similar analysis is then applied to the convergence field, the weighted projection of the matter density fluctuation field along the line of sight, with similar conclusions. We also show how simple mappings can correct for this inadequacy, consistently with previous findings in the literature (Abridged) .

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。

摘要：

英文摘要：

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