  We study one of the simplest covariant modified-gravity models based on the
Dvali-Gabadadze-Porrati (DGP) brane cosmology, a self-accelerating universe. In
this model gravitational leakage into extra dimensions is responsible of
late-time acceleration. We mainly focus on the effects of the model parameters
on the geometry and the age of universe. Also we investigate the evolution of
matter density perturbations in the modified gravity model, and obtain an
analytical expression for the growth index, $f$. We show that increasing
$\Omega_{r_c}$ leads to less growth of the density contrast $\delta$, and also
decreases the growth index. We give a fitting formula for the growth index at
the present time and indicate that dominant term in this expression verifies
the well-known approximation relation $f\simeq \Omega_m^{\gamma}$. As the
observational test, the new Supernova Type Ia (SNIa) Gold sample and Supernova
Legacy Survey (SNLS) data, size of baryonic acoustic peak from Sloan Digital
Sky Survey (SDSS), the position of the acoustic peak from the CMB observations
and the Cluster Baryon Gas Mass Fraction (gas) are used to constrain the
parameters of the DGP model. We also combine previous results with large scale
structure formation (LSS) from the 2dFGRS survey. Finally to check the
consistency of the DGP model, we compare the age of old cosmological objects
with age of universe in this model.
