A parametrization for the growth index of linear matter perturbations

Abstract

We propose a parametrization for the growth index of the linear matter perturbations, γ(z) = γ 0 + z 1+z γ 1 . The growth factor of the perturbations parameterized as Ω γ m is analyzed for both the wCDM model and the DGP model with our proposed form for γ. We find that γ 1 is negative for the wCDM model but is positive for the DGP model. Thus it provides another signature to discriminate them. We demonstrate that Ω γ m 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 ΛCDM 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.

Linear growth in power lawf(T)gravity

“…(46) As expected, for the Λ cosmology (b = 0) the above formula reduces to its standard expression [45][46][47][48][49]. Lastly, inserting γ 0 = γ ∞ − γ 1 into Eq.…”

“…(31) and (38). In this work we consider the most popular γ(a) parametrization that has appeared in the literature (see [45][46][47][48][49]), which is a Taylor expansion around a(z) = 1…”

Impact of dark energy perturbations on the growth index

“…It has been noted that in General Relativity the slope is positive [23,36,37]. For all clustering dark energy models that we have considered, the slope for the growth index is positive, γ b > 0 (see table II).…”

Growth index after the Planck results

“…Actually the possible running of this index was also considered; for the recent progress on a parametrized approach, please see [34]. The focus of this paper is to investigate the growth index in GR and MG theory.…”