The growth index of matter perturbations and modified gravity

We place tight constraints on the growth index $γ$ by using the recent growth history results of 2dFGRS, SDSS-LRG, VIMOS-VLT deep Survey (VVDS) and {\em WiggleZ} datasets. In particular, we investigate several parametrizations of the growth index $γ(z)$, by comparing their cosmological evolution using observational growth rate data at different redshifts. Utilizing a standard likelihood analysis we find that the use of the combined growth data provided by the 2dFGRS, SDSS-LRG, VVDS and {\em WiggleZ} galaxy surveys, puts the most stringent constraints on the value of the growth index. As an example, assuming a constant growth index we obtain that $γ=0.602\pm 0.055$ for the concordance $Λ$CDM expansion model. Concerning the Dvali-Gabadadze-Porrati gravity model, we find $γ=0.503\pm 0.06$ which is lower, and almost $3σ$ away, from the theoretically predicted value of $γ_{DGP}\simeq 11/16$. Finally, based on a time varying growth index we also confirm that the combined growth data disfavor the DGP gravity.

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