2005ApJ...633..603X

Three different methods of measuring cosmology with gamma-ray bursts (GRBs) have been proposed since a relation between the gamma-ray energy E_γof a GRB jet and the peak energy E_pof the νF_νspectrum 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_γ-E_prelation 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 Ω_M=0.15^+0.45_–0.13(1 σ) for a flat ΛCDM universe. In method II, to calculate the probability for some certain cosmology, contributions of all the possible E_γ-E_prelations 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<Ω_M<0.69 (1 σ) for a flat universe. In method III, to obtain the probability for some cosmology, contributions of all the possible E_γ-E_prelations associated with their unequal weights are considered. With this method, we obtain an inspiring constraint on the mass density 0.16<Ω_M<0.45 (1 σ) for a flat universe and χ²_dof=19.08/15=1.27 for the concordance model of Ω_M=0.27. Compared with the previous two methods, method III makes the observed 17 GRBs place much more stringent confidence intervals at the same confidence levels. Furthermore, we perform a Monte Carlo simulation and use a larger sample to investigate the cosmographic capabilities of GRBs with different methods. We find that a larger GRB sample could be used to effectively measure cosmology, no matter whether the E_γ-E_prelation is calibrated by low-z bursts or not. Ongoing observations of GRBs in the Swift era are expected to make the cosmological utility of GRBs progress from its babyhood into childhood.