A matter-dominated cosmological model with variable G and Lambda and its confrontation with observational data

In the framework of renormalization-group improved cosmologies, we analyze both theoretically and observationally the exact and general solution of the matter-dominated cosmological equations, by using the expression of the cosmological term as a function of the Newton parameter already determined by the integration method employed in a previous paper. A rough comparison between such a model and the concordance LambdaCDM model from the point of view of the magnitude-redshift relationship has been already considered, without showing any appreciable differences. Here we test our model by using astrophysical data (the Union2 type Ia supernovae (SNIa) dataset, the Hubble diagram constructed from some gamma ray bursts luminosity distance indicator), to constrain its parameters. We also apply a cosmographic approach to our cosmological model. In order to estimate the cosmographic parameters we fit a large dataset, including not only the Hubble diagram, as traced by SNIa and gamma ray bursts, but also the H(z) measurements from passively evolving galaxies, baryon acoustic oscillations and the distance priors from the cosmic microwave background radiation anisotropy spectrum. We show that this matter-dominated cosmological model with variable Newton parameter and variable cosmological term is indeed compatible with the observations above. The cosmographic approach adopted confirms such conclusions. Last, it seems possible to include radiation into the model, since numerical integration of the equations derived by the presence of both radiation and matter shows that, after inflation, the total density parameter is initially dominated by the radiation contribution and later by the matter one.