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

Three different methods of measuring cosmology with gamma-ray bursts (GRBs)have been proposed since a relation between the $\gamma$-ray energy $E_{\gamma}$ of a GRB jet and the peak energy $E_p$ of the $\nu F_{\nu}$ spectrum in theburst frame was reported by Ghirlanda and coauthors. In Method I, to calculatethe probability for a favored cosmology, only the contribution of the$E_\gamma-E_p$ relation that is already best fitted for this cosmology isconsidered. We apply this method to a sample of 17 GRBs, and obtain the massdensity $\Omega_M=0.15^{+0.45}_{-0.13}$ ($1\sigma$) for a flat $\Lambda$CDMuniverse. In Method II, to calculate the probability for some certaincosmology, contributions of all the possible $E_\gamma-E_p$ relations that arebest fitted for their corresponding cosmologies are taken into account. Withthis method, we find a constraint on the mass density $0.14<\Omega_M<0.69$ ($1\sigma$) for a flat universe. In Method III, to obtain the probability for somecosmology, contributions of all the possible $E_\gamma-E_p$ relationsassociated with their unequal weights are considered. With this method, weobtain an inspiring constraint on the mass density $0.16<\Omega_M<0.45$ ($1\sigma$) for a flat universe, and a $\chi^2_{dof}=19.08/15=1.27$ for theconcordance model of $\Omega_M=0.27$. (abridged)Comment: 26 pages including 6 figures, different methods compared, accepted for publication in Ap