从主成分分析重建哈勃参数：最小化偏差
Hubble parameter reconstruction from a principal component analysis: minimizing the bias
摘要：
一个独立于模型的宇宙膨胀率的重建对于宇宙学观测的可靠分析是必不可少的。我们的目标是证明，目前的数据能够提供合理的约束行为的哈勃参数红移，独立于任何宇宙学模型或基础引力理论。使用Ia型超新星的数据，我们表明，它是可能的分析计算的Fisher矩阵分量的哈勃参数分析没有假设的能量含量的宇宙。我们使用主成分分析来重建哈勃参数作为Fisher矩阵特征向量（主成分）的线性组合。为了抑制由组分的高红移行为引入的偏置，我们将高红移处的哈勃参数值视为自由参数。我们首先使用Ia型超新星观测的模拟样本测试了我们的程序，然后将其应用于斯隆数字巡天（SDSS）小组编制的真实数据。在模拟样品分析中，我们证明，它是可能的，以大大抑制由主成分的高红移行为所引入的偏见。应用我们的程序的真实数据，我们表明，它使我们能够确定合理的不确定性的哈勃参数的行为，而不引入任何特设参数化。除此之外，我们的重建同意完全独立的测量哈勃参数获得的红包星系。
英文摘要：
A model-independent reconstruction of the cosmic expansion rate is essential to a robust analysis of cosmological observations. Our goal is to demonstrate that current data are able to provide reasonable constraints on the behavior of the Hubble parameter with redshift, independently of any cosmological model or underlying gravity theory. Using type Ia supernova data, we show that it is possible to analytically calculate the Fisher matrix components in a Hubble parameter analysis without assumptions about the energy content of the Universe. We used a principal component analysis to reconstruct the Hubble parameter as a linear combination of the Fisher matrix eigenvectors (principal components). To suppress the bias introduced by the high redshift behavior of the components, we considered the value of the Hubble parameter at high redshift as a free parameter. We first tested our procedure using a mock sample of type Ia supernova observations, we then applied it to the real data compiled by the Sloan Digital Sky Survey (SDSS) group. In the mock sample analysis, we demonstrate that it is possible to drastically suppress the bias introduced by the high redshift behavior of the principal components. Applying our procedure to the real data, we show that it allows us to determine the behavior of the Hubble parameter with reasonable uncertainty, without introducing any ad-hoc parameterizations. Beyond that, our reconstruction agrees with completely independent measurements of the Hubble parameter obtained from red-envelope galaxies.
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