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arXiv 1310.6038astro-ph.CO
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星系巡天中大尺度结构的充分观测量

Sufficient observables for large scale structure in galaxy surveys

Julien Carron, Istvan Szapudi

摘要:

在线性区域之外,物质场的功率谱和高阶矩不再捕捉到所有编码在密度涨落中的宇宙学信息。虽然已经提出了非线性变换来提取传统方法所丢失的信息,但到目前为止,将这些技术推广到离散过程的方法还不清楚;特别扩展取得了一些成功。我们在Carron和Szapudi(2013)中指出,对数变换非常好地近似了最佳的“充分统计”,即从(连续)物质场提取所有信息的可观测量。在这些结果的基础上,我们将最佳变换推广到离散星系场。我们专注于我们的计算上的泊松抽样的对数正态密度场。我们解决和测试的一点的情况下,详细,并勾勒出充分的可观的多点的情况下。此外,我们提出了一个精确的近似的充分可观的非线性变换场的平均值和频谱。我们发现,相应的最佳非线性变换直接与Kitaura等人(2010)提出的具有对数正态先验的基础连续场的最大后验贝叶斯重建有关。因此,简单的食谱,实现足够的可观的,可以建立在以前提出的算法,已成功实施和测试的模拟。

英文摘要:

Beyond the linear regime, the power spectrum and higher order moments of the matter field no longer capture all cosmological information encoded in density fluctuations. While non-linear transforms have been proposed to extract this information lost to traditional methods, up to now, the way to generalize these techniques to discrete processes was unclear; ad hoc extensions had some success. We pointed out in Carron and Szapudi (2013) that the logarithmic transform approximates extremely well the optimal "sufficient statistics", observables that extract all information from the (continuous) matter field. Building on these results, we generalize optimal transforms to discrete galaxy fields. We focus our calculations on the Poisson sampling of an underlying lognormal density field. We solve and test the one-point case in detail, and sketch out the sufficient observables for the multi-point case. Moreover, we present an accurate approximation to the sufficient observables in terms of the mean and spectrum of a non-linearly transformed field. We find that the corresponding optimal non-linear transformation is directly related to the maximum a posteriori Bayesian reconstruction of the underlying continuous field with a lognormal prior as put forward in Kitaura et al (2010). Thus simple recipes for realizing the sufficient observables can be built on previously proposed algorithms that have been successfully implemented and tested in simulations.

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