Dynamic of the accelerated expansion of the universe in the DGP model

According to experimental data of SNe Ia (Supernovae type Ia), we will discuss in detial dynamics of the DGP model and introduce a simple parametrization of matter $ω$, in order to analyze scenarios of the expanding universe and the evolution of the scale factor. We find that the dimensionless matter density parameter at the present epoch $Ω^0_m=0.3$, the age of the universe $t_0= 12.48$ Gyr, $\frac{a}{a_0}=-2.4e^{\frac{-t}{25.56}}+2.45$. The next we study the linear growth of matter perturbations, and we assume a definition of the growth rate, $f \equiv \frac{dlnδ}{dlna}$. As many authors for many years, we have been using a good approximation to the growth rate $f \approx Ω^{γ(z)}_m$, we also find that the best fit of the growth index, $γ(z)\approx 0.687 - \frac{40.67}{1 + e^{1.7. (4.48 + z)}}$, or $γ(z)= 0.667 + 0.033z$ when $z\ll1$. We also compare the age of the universe and the growth index with other models and experimental data. We can see that the DGP model describes the cosmic acceleration as well as other models that usually refers to dark energy and Cold Dark Matter (CDM).