| Abstract
| - Gamma-ray bursts (GRBs) have recently attracted much attention as a possible way to extend the Hubble diagram (HD) 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-parameter correlations and using a fiducial cosmological model to calibrate them, Schaefer has compiled a sample of 69 GRBs with measured μ(z) which has since then been widely used to constrain cosmological parameters. Here, we update this sample through many aspects. First, we add a recently found correlation to the X-ray afterglow and use a Bayesian-inspired fitting method to calibrate the different GRB correlations known so far by assuming a fiducial Λ cold dark matter model in agreement with the recent Wilkinson Microwave Anisotropy Probe5 data. Averaging over six correlations, we end up with a new GRB HD 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 Type Ia Supernovae sample to calibrate the GRBs correlations. This finally gives us a GRB HD made out of 69 GRBs whose estimated distance modulus μ(z) is almost independent of the underlying cosmological model.
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