Observational constraints to a unified cosmological model

We propose a phenomenological unified model for dark matter and dark energy based on an equation of state parameter $w$ that scales with the $\arctan$ of the redshift. The free parameters of the model are three constants: $\Omega_{b0}$, $\alpha$ and $\beta$. Parameter $\alpha$ dictates the transition rate between the matter dominated era and the accelerated expansion period. The ratio $\beta / \alpha$ gives the redshift of the equivalence between both regimes. Cosmological parameters are fixed by observational data from Primordial Nucleosynthesis (PN), Supernovae of the type Ia (SNIa), Gamma-Ray Bursts (GRB) and Baryon Acoustic Oscillations (BAO). The calibration of the 138 GRBs events is performed using the 580 SNIa of the Union2.1 data set and a new set of 79 high-redshift GRBs is obtained. The various sets of data are used in different combinations to constraint the parameters through statistical analysis. The unified model is compared to the $\Lambda$CDM model and their differences are emphasized.