Observational tests of the Glavan, Prokopec and Starobinsky model of
  dark energy
  In the last dozens of years different data sets revealed the accelerated
expansion of the Universe which is driven by the so called dark energy, that
now dominates the total amount of matter-energy in the Universe. In a recent
paper Glavan, Prokopec and Starobinsky propose an interesting model of dark
energy, which traces the Universe evolution from the very early quantum era to
the present time. Here we perform a high-redshift analysis to check if this new
model is compatible with present day observational data and compare predictions
of this model with that of the standard $\Lambda$CDM cosmological model. In our
analysis we use only the most reliable observational data, namely the distances
to selected SNIa, GRB Hubble diagram, and $28$ direct measurements of the
Hubble constant. Moreover we consider also non {\it geometric} data related to
the growth rate of density perturbations. We explore the probability
distributions of the cosmological parameters for both models. To build up their
own regions of confidence, we maximize the appropriate likelihood functions
using the Markov chain Monte Carlo (MCMC) method. Our statistical analysis
indicates that these very different models of dark energy are compatible with
present day observational data and the GPS model seems slightly favored with
respect to the $\Lambda$CDM model. However to further restrict different models
of dark energy it will be necessary to increase the precision of the Hubble
diagram at high redshifts and to perform more detailed analysis of the
influence of dark energy on the process of formation of large scale structure.
