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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 $γ$ as a function of redshift. At the linear approximation: $γ(z)\approxγ_0+γ_0^\prime z $, we find that, for $0.2\leqΩ_{m,0}\leq0.35$, $γ_0$ takes the value from 0.658 to 0.671, and $γ_0^\prime$ ranges from 0.035 to 0.042. With three low redshift observational data of the growth factor, we obtain the observational constraints on $γ_0$ and $γ_0'$ for the $ΛCDM$ and DGP models and find that the observations favor the $ΛCDM$ model but at the $1σ$ confidence level both the $ΛCDM$ and DGP models are consistent with the observations.