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 $γ$-ray energy $E_γ $ of a GRB jet and the peak energy $E_p$ of the $νF_ν$ 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 $E_γ-E_p$ 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 $Ω_M=0.15^{+0.45}_{-0.13}$ ($1σ$) for a flat $Λ$CDM universe. In Method II, to calculate the probability for some certain cosmology, contributions of all the possible $E_γ-E_p$ relations that are best fitted for their corresponding cosmologies are taken into account. With this method, we find a constraint on the mass density $0.14<Ω_M<0.69$ ($1 σ$) for a flat universe. In Method III, to obtain the probability for some cosmology, contributions of all the possible $E_γ-E_p$ relations 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 a $χ^2_{dof}=19.08/15=1.27$ for the concordance model of $Ω_M=0.27$. (abridged)