Can Gamma-Ray Bursts Be Used to Measure Cosmology? A Further Analysis

Abstract

Three different methods of measuring cosmology with gamma-ray bursts (GRBs) have been proposed since a relation between the ${\hat{I}}^3$-ray energy $E_{\hat{I}}^3$ of a GRB jet and the peak energy $E_p$ of the $\hat{I}½F_{\hat{I}}½$ spectrum in the burst frame was reported by Ghirlanda and coauthors. In Method I, to calculate the probability for a favored cosmology, only the contribution of the $E_{\hat{I}}^3-E_p$ relation that is already best fitted for this cosmology is considered. We apply this method to a sample of 17 GRBs, and obtain the mass density $\hat{I}{\text{c◯}}_M=0.15_{-0.13}^{+0.45}$ ($1\ddot{I}ƒ$) for a flat $\hat{I}›$CDM universe. In Method II, to calculate the probability for some certain cosmology, contributions of all the possible $E_{\hat{I}}^3-E_p$ relations that are best fitted for their corresponding cosmologies are taken into account. With this method, we find a constraint on the mass density $0.14<\hat{I}{\text{c◯}}_M<0.69$ ($1\ddot{I}ƒ$) for a flat universe. In Method III, to obtain the probability for some cosmology, contributions of all the possible $E_{\hat{I}}^3-E_p$ relations associated with their unequal weights are considered. With this method, we obtain an inspiring constraint on the mass density $0.16<\hat{I}{\text{c◯}}_M<0.45$ ($1\ddot{I}ƒ$) for a flat universe, and a $\ddot{I}{‡}_{dof}^2=19.08/15=1.27$ for the concordance model of $\hat{I}{\text{c◯}}_M=0.27$. (abridged)

26 pages including 6 figures, different methods compared, accepted for publication in ApJ