The growth of linear perturbations in the DGP model

Abstract

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 $0.2\le {\Omega }_{m,0}\le 0.35$, ${\gamma }_0$ 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 ${\gamma }_0^{\prime }$ 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.

12 pages, 4 figuers, to appear in PLB

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