The Djorgovski-Gurzadyan dark energy integral equation and the Hubble
  diagram
  We consider the observational aspects of the value of dark energy density
from quantum vacuum fluctuations based initially on the Gurzadyan-Xue model. We
reduce the Djorgovski-Gurzadyan integral equation to a differential equation
for the co-moving horizon and then, by means of the obtained explicit form for
the luminosity distance, we construct the Hubble diagram for two classes of
observational samples. For supernova and gamma-ray burst data we show that this
approach provides viable predictions for distances up to $z \simeq 9$,
quantitatively at least as good as those provided by the lambda cold dark
matter ($\Lambda$CDM) model. The Hubble parameter dependence $H(z)$ of the two
models also reveals mutual crossing at $z=0.4018$, the interpretation of which
is less evident.
