2008ApJ...680...92L

Due to the lack of low-redshift long gamma-ray bursts (GRBs), the circular problem has been a severe obstacle for using GRBs as cosmological candles. In this paper, we present a new method to deal with such a problem in Markov chain Monte Carlo (MCMC) global fitting analysis. Assuming a certain type of correlation, for the parameters involved in the correlation relation, we treat them as free parameters and determine them simultaneously with cosmological parameters through MCMC analysis on GRB data together with other observational data. Then the circular problem is naturally eliminated in this procedure. To demonstrate the feasibility of our method, we take the Ghirlanda relation (E_γ∝CE^A_peak) as an example, while keeping in mind the debate about its physical validity. Together with SN Ia, WMAP, and SDSS data, we include 27 GRBs with the reported Ghirlanda relation in our study and perform MCMC global fitting. We consider the ΛCDM model and dynamical dark energy models, respectively. We also include the curvature of the universe in our analysis. In each case, in addition to the constraints on the relevant cosmological parameters, we obtain the best-fit values as well as the distributions of the correlation parameters A and C. With CMB+LSS+SNe+GRB data included in the analysis, the results on A and C for different cosmological models are in agreement well within a 1 σ range. It is also noted that the distributions of A and C are generally broader than the priors used in many studies in the literature. Our method can be readily applied to other GRB relations, which might be better physically motivated.