A parametrization for the growth index of linear matter perturbations

Abstract

We propose a parametrization for the growth index of the linearmatter perturbations, γ(z) = γ0 + [z/(1+z)]γ1.The growth factor of the perturbations parameterized asΩmγ is analyzed for both the wCDM model and theDGP model with our proposed form for γ. We find thatγ1 is negative for the wCDM model but is positive for theDGP model. Thus it provides another signature to discriminate them.We demonstrate that Ωmγ with γ taking ourproposed form approximates the growth factor very well both at lowand high redshfits for both kinds of models. In fact, the error isbelow 0.03% for the ΛCDM model and 0.18% for the DGPmodel for all redshifts when Ωm0 = 0.27. Therefore, ourparametrization may be robustly used to constrain the growth indexof different models with the observational data which include pointsfor redshifts ranging from 0.15 to 3.8, thus providingdiscriminative signatures for different models.