  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 $\omega$, 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 $\Omega^0_m=0.3$,
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,
$f \equiv \frac{dln\delta}{dlna}$. As many authors for many years, we have been
using a good approximation to the growth rate $f \approx \Omega^{\gamma(z)}_m$,
we also find that the best fit of the growth index, $\gamma(z)\approx 0.687 -
\frac{40.67}{1 + e^{1.7. (4.48 + z)}}$, or $\gamma(z)= 0.667 + 0.033z$ 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).
