The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts
  One of the few ways to measure the properties of Dark Energy is to extend the Hubble daigram (HD) to higher redshifts with Gamma-Ray Bursts (GRBs). GRBs have at least five properties (their spectral lag, variability, spectral peak photon energy, time of the jet break, and the minimum rise time) which have correlations to the luminosity of varying quality. In this paper, I construct a GRB HD with 69 GRBs over a redshift range of 0.17 to >6, with half the bursts having a redshift larger than 1.7. This paper uses over 3.6 times as many GRBs and 12.7 times as many luminosity indicators as any previous GRB HD work. For the gravitational lensing and Malmquist biases, I find that the biases are small, with an average of 0.03 mag and an RMS scatter of 0.14 mag in the distance modulus. The GRB HD is well-behaved and nicely delineates the shape of the HD. The reduced chi-square for the fit to the concordance model is 1.05 and the RMS scatter about the concordance model is 0.65 mag. This accuracy is just a factor of 2.0 times that gotten for the same measure from all the big supernova surveys. I fit the GRB HD to a variety of models, including where the Dark Energy has its equation of state parameter varying as w(z)=w_0 + w_a z/(1+z). I find that the concordance model is consistent with the data. That is, the Dark Energy can be described well as a Cosmological Constant that does not change with time. (abridged) 
Bradley E. Schaefer