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 _ { h } = ct Universe and find that the optimal \Lambda CDM model fits the GRB Hubble Diagram with a reduced \chi ^ { 2 } _ { dof } \approx 2.26 , whereas the fit using R _ { h } = ct results in a \chi ^ { 2 } _ { 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 _ { h } = ct being closer to the correct model is \sim 85 - 96 \% , compared to \sim 4 - 15 \% for \Lambda CDM .