The growth of linear perturbations in the DGP model

We study the linear growth of matter perturbations in the DGP model with the growth index $\gamma$ as a function of redshift. At the linear approximation: $\gamma(z)\approx\gamma_0+\gamma_0^\prime z $, we find that, for $0.2\leq\Omega_{m,0}\leq0.35$, $\gamma_0$ takes the value from 0.658 to 0.671, and $\gamma_0^\prime$ ranges from 0.035 to 0.042. With three low redshift observational data of the growth factor, we obtain the observational constraints on $\gamma_0$ and $\gamma_0'$ for the $\Lambda CDM$ and DGP models and find that the observations favor the $\Lambda CDM$ model but at the $1\sigma$ confidence level both the $\Lambda CDM$ and DGP models are consistent with the observations.