SIMBAD references

It has been recently empirically established that some of the directly observed parameters of gamma-ray bursts (GRBs) are correlated with their important intrinsic parameters, such as the luminosity or the total radiated energy. These correlations were derived, tested and used to standardize GRBs, i.e. to derive their luminosity or radiated energy from one or more observables, in order to construct an estimated fiducial Hubble diagram (HD), assuming that radiation propagates in the standard Λ cold dark matter cosmological model. We extend these analyses by considering more general models of dark energy and an updated data set of high-redshift GRBs. We show that the correlation parameters only weakly depend on the cosmological model. Moreover we apply a local regression technique to estimate, in a model-independent way, the distance modulus from the recently updated Type Ia supernova (SNIa) sample containing 307 SNIa, in order to calibrate the GRBs 2D correlations, by considering only GRBs with z≤ 1.4. The derived calibration parameters are used to construct a new GRBs HD, which we call the calibrated GRBs HD. We also compare the estimated and calibrated GRBs HDs. It turns out that for the common GRBs they are fully statistically consistent, thus indicating that both of them are not affected by any systematic bias induced by the different standardizing procedures. We finally apply our methods to calibrate 95 long GRBs with the well-known Amati relation and construct the estimated and calibrated GRBs HD that extends to redshifts z∼ 8. Even in this case there is consistency between these data sets. This means that the high-redshift GRBs can be used to test different models of dark energy. We used the calibrated GRBs HD to constrain our quintessential cosmological model and derived the likelihood values of Ω_m and w(0).