The Gamma-Ray Burst Hubble Diagram and Its Cosmological Implications
  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 lightcurve features can
indeed be used as luminosity indicators, and demonstrate from the most
up-to-date GRB sample appropriate for this work that the $\Lambda$CDM model
optimized with these data is characterized by parameter values consistent with
those in the concordance model. Specifically, we find that
$(\Omega_m,\Omega_\Lambda)\approx (0.25_{-0.06}^{+0.05},
0.75_{-0.05}^{+0.06})$, which are consistent, to within $1\sigma$, with
$(0.29,0.71)$ obtained from the 9-yr WMAP data. We also carry out a comparative
analysis between $\Lambda$CDM and the $R_{\rm h}=ct$ Universe and find that the
optimal $\Lambda$CDM model fits the GRB Hubble Diagram with a reduced
$\chi^2_{\rm dof}\approx 2.26$, whereas the fit using $R_{\rm h}=ct$ results in
a $\chi^2_{\rm dof}\approx 2.14$. In both cases, about 20% of the events lie at
least $2\sigma$ 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 (AIC), the Kullback Information Criterion (KIC), and the
Bayes Information Criterion (BIC)---to show that, based on the GRB Hubble
Diagram, the likelihood of $R_{\rm h}=ct$ being closer to the correct model is
$\sim 85-96%$, compared to $\sim 4-15%$ for $\Lambda$CDM.
