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 Ep of the (nu)F(nu) 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(gamma)-Ep 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 (omega)M = 0.15... (1 (sigma)) for a flat (lambda)CDM universe. In method II, to calculate the probability for some certain cosmology, contributions of all the possible E(gamma)-Ep 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 < (omega)M < 0.69 (1 (sigma)) for a flat universe. In method III, to obtain the probability for some cosmology, contributions of all the possible E(gamma)-Ep relations associated with their unequal weights are considered. With this method, we obtain an inspiring constraint on the mass density 0.16 < (omega)M < 0.45 (1 (sigma)) for a flat universe and (chi)...= 19.08/15 = 1.27 for the concordance model of (omega)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(gamma)-Ep relation 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.