A parametrization for the growth index of linear matter perturbations

We propose a parametrization for the growth index of the linear matter perturbations, $γ(z)=γ_0+\frac{z}{1+z}γ_1$. The growth factor of the perturbations parameterized as $Ω_m^γ$ is analyzed for both the $w$CDM model and the DGP model with our proposed form for $γ$. We find that $γ_1$ is negative for the $w$CDM model but is positive for the DGP model. Thus it provides another signature to discriminate them. We demonstrate that $Ω_m^γ$ with $γ$ taking our proposed form approximates the growth factor very well both at low and high redshfits for both kinds of models. In fact, the error is below 0.03% for the $Λ$CDM model and 0.18% for the DGP model for all redshifts when $Ω_{m0}=0.27$. Therefore, our parametrization may be robustly used to constrain the growth index of different models with the observational data which include points for redshifts ranging from 0.15 to 3.8, thus providing discriminative signatures for different models.

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