An updated Gamma Ray Bursts Hubble diagram

Gamma ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram to very high redshift. To this aim, the luminosity (or isotropic emitted energy) of a GRB at redshift z must be evaluated from a correlation with a distance independent quantity so that one can then solve for the luminosity distance DL(z) and hence the distance modulus μ(z). Averaging over five different two parameters correlations and using a fiducial cosmological model to calibrate them, Schaefer (2007) has compiled a sample of 69 GRBs with measured μ(z) which has since then been widely used to constrain cosmological parameters. We update here that sample by many aspects. First, we add a recently found correlation for the X ray afterglow and use a Bayesian inspired fitting method to calibrate the different GRBs correlations known insofar assuming a fiducial ΛCDM model in agreement with the recent WMAP5 data. Averaging over six correlations, we end with a new GRBs Hubble diagram comprising 83 objects. We also extensively explore the impact of varying the fiducial cosmological model considering how the estimated μ(z) change as a function of the (ΩM , w0, wa) parameters of the Chevallier Polarski Linder phenomenological dark energy equation of state. In order to avoid the need of assuming an a priori cosmological model, we present a new calibration procedure based on a model independent local regression estimate of μ(z) using the Union SNeIa sample to calibrate the GRBs correlations. This finally gives us a GRBs Hubble diagram made out of 69 GRBs whose estimated distance modulus μ(z) is almost independent on the underlying cosmological model.