论文标题
随着时间的推移，对两个宇宙参数的测量值进行了卡方分析
A Chi-Squared Analysis of the Measurements of Two Cosmological Parameters Over Time
论文作者
论文摘要
该分析的目的是确定给定的误差线是否真正代表了两个宇宙学参数的历史汇编中值的分散：质量波动的幅度（$σ_8$）和Hubble的常数（$ H_0 $）参数在标准宇宙学模型中。对于此分析，在过去的测量列表中执行了卡方测试。通过分析$σ_8$（1993年至2019年之间测量的60个数据点的卡方（$χ^2 $）值的分析（$χ^2 $）值，以及182.4和189.0之间的$χ^2 $）相关的概率q极低，$ q = 1.6 \ times 10^{ - 15} $ nimec = 8.8 fit的$ q = 1.6 \ time $ q = 8.8 fit， 数据。对于$ H_0 $的$χ^2 $值（1976年至2019年之间测量的163个数据点，480.1和575.7之间的$χ^2 $）也是如此，其中$ q = 1.8 \ times 10^{ - 33} $用于数据的线性拟合和$ q = 1.0 \ q = 1.0 \ Q = 1.0 \ Q = 1.0 \ Q = 1.0 \ times 10^{ - 47} $的平均水平。一般的结论是，与观察到的参数测量相关的统计误差线已经被低估了，或者在至少20 \％的测量中未正确考虑系统误差。 〜$ h_0 $的错误条低估的事实是如此普遍，可能会解释明显的4.4 $σ$差异，如今正式被称为哈勃张力。
The aim of this analysis was to determine whether or not the given error bars truly represented the dispersion of values in a historical compilation of two cosmological parameters: the amplitude of mass fluctuations ($σ_8$) and Hubble's constant ($H_0$) parameters in the standard cosmological model. For this analysis, a chi-squared test was executed on a compiled list of past measurements. It was found through analysis of the chi-squared ($χ^2$) values of the data that for $σ_8$ (60 data points measured between 1993 and 2019 and $χ^2$ between 182.4 and 189.0) the associated probability Q is extremely low, with $Q = 1.6 \times 10^{-15}$ for the weighted average and $Q = 8.8 \times 10^{-15}$ for the best linear fit of the data. This was also the case for the $χ^2$ values of $H_0$ (163 data points measured between 1976 and 2019 and $χ^2$ between 480.1 and 575.7), where $Q = 1.8 \times 10^{-33}$ for the linear fit of the data and $Q = 1.0 \times 10^{-47}$ for the weighted average of the data. The general conclusion was that the statistical error bars associated with the observed parameter measurements have been underestimated or the systematic errors were not properly taken into account in at least 20\% of the measurements. The~fact that the underestimation of error bars for $H_0$ is so common might explain the apparent 4.4$σ$ discrepancy formally known today as the Hubble tension.
