Systematics in the Gamma Ray Bursts Hubble diagram
  Thanks to their enormous energy release which allows to detect them up to
very high redshift, Gamma Rays Bursts (GRBs) have recently attracted a lot of
interest to probe the Hubble diagram (HD) deep into the matter dominated era
and hence complement Type Ia Supernoave (SNeIa). However, lacking a local GRBs
sample, calibrating the scaling relations proposed as an equivalent to the
Phillips law to standardize GRBs is not an easy task because of the need to
estimate the GRBs luminosity distance in a model independent way. We consider
here three different calibration methods based on the use of a fiducial
$\Lambda$CDM model, on cosmographic parameters and on the local regression on
SNeIa. We find that the calibration coefficients and the intrinsic scatter do
not significantly depend on the adopted calibration procedure. We then
investigate the evolution of these parameters with the redshift finding no
statistically motivated improvement in the likelihood so that the no evolution
assumption is actually a well founded working hypothesis. Under this
assumption, we then consider possible systematics effects on the HDs introduced
by the calibration method, the averaging procedure and the homogeneity of the
sample arguing against any significant bias. We nevertheless stress that a
larger GRBs sample with smaller uncertainties is needed to definitely conclude
that the different systematics considered here have indeed a negligible impact
on the HDs thus strengthening the use of GRBs as cosmological tools.
