Hubble diagram of gamma-ray bursts calibrated with Gurzadyan-Xue cosmology

Context. Because gamma-ray bursts (GRBs) are the most luminous among known cosmic objects, they carry an essential potential for cosmological studies if properly used as standard candles. Aims. We used GRBs to test the cosmological predictions of the Gurzadyan-Xue (GX) model of dark energy, a novel theory that predicts, without any free parameters, the current vacuum fluctuation energy density close to the value inferred from the SNIa observations. We also compared the GX results with those predicted by the concordance scenario Λ-CDM. Methods. After a consistent calibration for a specific model, using the several empirical relations obtained from GRBs observables enables one to probe current cosmological models. Based on this recently introduced method, we used several samples from different sources that fit our needs, including 69 GRBs, the recently released SWIFT satellite data, and 41 GRBs that have firmly determined redshifts. These data samples span a distance scale up to redshift about 7. Results. We show that the GX models are compatible with the Hubble diagram of the 69 GRBs sample. Such an adjustment is almost identical to the one for the concordance Λ-CDM. From this particular analysis, we can obtain the corresponding values of the matter density parameter $\Omega_{\rm m}$ describing GX models. When the same procedure is applied to the SWIFT satellite data, we verify that the SWIFT sample does not delineate a Hubble diagram as clearly as featured by the 69 GRBs sample. Conclusions. The analysis of these 3 samples shows that more data and effort are needed to elucidate both issues: the gamma-ray bursts/standard-candle and the lack of a theoretical understanding of the physics that may explain the empirical relations