论文标题
高斯副群的改进的AMATI相关性
The improved Amati correlations from Gaussian copula
论文作者
论文摘要
在本文中，我们通过强大的称为Copula的强大统计工具获得了伽马射线爆发（GRB）数据的两个改进的AMATI相关性。校准后，使用低频GRB数据，基于基于$ω__\ MathRM {M0} = 0.3 $和$ H_0 = 70〜 \ Mathrm {km〜s^s^{-1} mpc^{ - 1} mpc^{ - 1} $的AMATI相关性改进了AMATI相关性。获取GRB数据点的Hubble图。应用这些GRB数据来限制$λ$ CDM型号，我们发现Copula的改进的AMATI相关性可以使结果与$ω__\ Mathrm {M0} = 0.3 $一致，而标准的Amati和扩展的Amati相关性则没有。该结果表明，当在低频校准方法中使用了Copula的改进AMATI相关性时，GRB数据可以视为可行的宇宙探索者。但是，贝叶斯信息标准表明，由于模型参数最少，因此标准的AMATI相关性仍然有些偏爱。此外，一旦使用了同时拟合方法而不是使用低降射校准的方法，就没有明显的证据表明改进的AMATI相关性优于标准相关性。因此，将来需要做更多的工作才能比较不同的AMATI相关性。
In this paper, we obtain two improved Amati correlations of the Gamma-Ray burst (GRB) data via a powerful statistical tool called copula. After calibrating, with the low-redshift GRB data, the improved Amati correlations based on a fiducial $Λ$CDM model with $Ω_\mathrm{m0}=0.3$ and $H_0=70~\mathrm{km~s^{-1}Mpc^{-1}}$, and extrapolating the results to the high-redshift GRB data, we obtain the Hubble diagram of GRB data points. Applying these GRB data to constrain the $Λ$CDM model, we find that the improved Amati correlation from copula can give a result well consistent with $Ω_\mathrm{m0}=0.3$, while the standard Amati and extended Amati correlations do not. This results suggest that when the improved Amati correlation from copula is used in the low-redshift calibration method, the GRB data can be regarded as a viable cosmological explorer. However, the Bayesian information criterion indicates that the standard Amati correlation remains to be favored mildly since it has the least model parameters. Furthermore, once the simultaneous fitting method rather than the low-redshift calibration one is used, there is no apparent evidence that the improved Amati correlation is better than the standard one. Thus, more works need to be done in the future in order to compare different Amati correlations.
