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 D_L(z) and hence the distance
modulus mu(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 mu(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 LCDM 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
mu(z) change as a function of the $(\Omega_M, w_0, w_a)$ parameters of the
Chevallier - Polarski - Linder phenomenological dark energy equation of state.
In order to avoid the need of assuming an {\it a priori} cosmological model, we
present a new calibration procedure based on a model independent local
regression estimate of mu(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 mu(z) is almost independent on the underlying
cosmological model.
