SIMBAD references

We present the constraints on the cosmological parameters obtained with the E_peak-E_γ correlation found with the most recent sample of 19 GRBs with spectroscopically measured redshift and well determined prompt emission spectral and afterglow parameters. We compare our results obtained in the two possible uniform jet scenarios, i.e. assuming a homogeneous density profile (HM) or a wind density profile (WM) for the circumburst medium. We explore the improvements to the constraints of the cosmological parameters that could be reached with a large sample, ∼150 GRBs, in the future. Finally, we study the possibility to calibrate the slope of these correlations. Our optimization analysis suggests that ∼12 GRBs with redshift z∈(0.9,1.1) can be used to calibrate the E_peak-E_γ with a precision better than 1%. The same precision is expected for the same number of bursts with z∈(0.45,0.75). This result suggests that we do not necessarily need a large sample of low z GRBs for calibrating the slope of these correlations.