The improved Amati correlations from Gaussian copula

TL;DR

This paper introduces improved Amati correlations for gamma-ray burst data using copula, enhancing their utility in cosmological measurements and providing a new statistical approach to analyze GRB correlations.

Contribution

The paper develops and applies copula-based methods to improve Amati correlations, offering a novel statistical technique for GRB data analysis in cosmology.

Findings

Improved Amati correlation aligns well with the standard cosmological model.

Standard Amati correlation remains mildly favored by Bayesian information criterion.

No clear evidence that the improved correlation outperforms the standard one in all methods.

Abstract

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 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.