The improved Amati correlations from Gaussian copula

Yang Liu, Fuyong Chen, Nan Liang, Zunli Yuan, Hongwei Yu, Puxun Wu1

Published 2022-03-07Version 1

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 $\Lambda$CDM model with $\Omega_\mathrm{m0}=0.3$ 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 $\Lambda$CDM model, we find that the improved Amati correlation from copula can give a result well consistent with $\Omega_\mathrm{m0}=0.3$, while the original Amati and extended Amati correlations do not. Our results suggest that when the improved Amati correlation from copula is used, the GRB data can be regarded as a viable cosmological explorer, and the copula method is a very powerful tool to study the distance correlations of cosmological data.