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In the framework of renormalization-group improved cosmologies, we analyzeboth theoretically and observationally the exact and general solution of thematter-dominated cosmological equations, using the expression of \Lambda =\Lambda(G) already determined by the integration method employed in a previouspaper. A rough comparison between such a model and the concordance \LambdaCDMmodel as to the magnitude-redshift relationship has been already done, withoutshowing any appreciable differences. We here perform a more refined study ofhow astrophysical data (Union2 set) on type-I supernovae, gamma ray bursts (ina sample calibrated in a model independent way with the SneIa dataset), and gasfraction in galaxy clusters (using a sample of Chandra measurements of theX-ray gas mass fraction) affect the model and constrain its parameters. We alsoapply a cosmographic approach to our cosmological model and estimate thecosmographic parameters by fitting both the supernovae and the gamma ray burstsdatasets. We show that this matter-dominated cosmological model with variableNewton parameter and variable cosmological term is indeed compatible with theobservations above (on type Ia supernovae, the gamma ray bursts Hubble diagram,and the gas mass fraction in X-ray luminous galaxy clusters). The cosmographicapproach adopted confirms such conclusions. Finally, it seems possible toinclude radiation into the model, since numerical integration of the equationsderived by the presence of both radiation and matter shows that, afterinflation, the total density parameter is initially dominated by the radiationcontribution and later by the matter one.

A matter-dominated cosmological model with variable $G$ and $\Lambda$. Confrontation of theoretical predictions with observational data