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 ≃ 9, quantitatively at least as good as those provided by the Λ cold dark matter 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