2013ApJ...772...43W

In this paper, we continue to build support for the proposal to use gamma-ray bursts (GRBs) as standard candles in constructing the Hubble diagram at redshifts beyond the current reach of Type Ia supernova observations. We confirm that correlations among certain spectral and light-curve features can indeed be used as luminosity indicators, and demonstrate from the most up-to-date GRB sample appropriate for this work that the ΛCDM model optimized with these data is characterized by parameter values consistent with those in the concordance model. Specifically, we find that (Ω_m, Ω_Λ) ≈ (0.25_–0.06^+0.05, 0.75 _–0.05^+0.06), which are consistent, to within 1σ, with (0.29, 0.71) obtained from the 9 yr Wilkinson Microwave Anisotropy Probe data. We also carry out a comparative analysis between ΛCDM and the R_h= ct universe and find that the optimal ΛCDM model fits the GRB Hubble diagram with a reduced Χ_dof² ≈ 2.26, whereas the fit using R_h= ct results in a Χ_dof² ≈ 2.14. In both cases, about 20% of the events lie at least 2σ away from the best-fit curves, suggesting that either some contamination by non-standard GRB luminosities is unavoidable or that the errors and intrinsic scatter associated with the data are being underestimated. With these optimized fits, we use three statistical tools–the Akaike information criterion, the Kullback information criterion, and the Bayes information criterion–to show that, based on the GRB Hubble diagram, the likelihood of R_h= ct being closer to the correct model is ∼85%-96%, compared to ∼4%-15% for ΛCDM.