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.