  Gamma-ray bursts (GRBs) being the most luminous among known cosmic objects
carry an essential potential for cosmological studies if properly used as
standard candles. In this paper we test with GRBs 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 compare the GX
results with those predicted by the concordance scenario $\Lambda$-CDM.
According to the statistical approach by Schaefer (2007), the use of several
empirical relations obtained from GRBs observables, after a consistent
calibration for a specific model, enables one to probe current cosmological
models. Based on this recently introduced method, we use the 69 GRBs sample
collected by Schaefer (2007); and the most recently released SWIFT satellite
data (Sakamoto et al. 2007) together with the 41 GRBs sample collected by
Rizzuto et al. (2007), which has the more firmly determined redshifts. Both
data samples span a distance scale up to redshift about 7. We show that the GX
models are compatible with the Hubble diagram of the Schaefer (2007) 69 GRBs
sample. Such adjustment is almost identical to the one for the concordance
$\Lambda$-CDM.
