A parametrization for the growth index of linear matter perturbations

TL;DR

This paper introduces a new parametrization for the growth index of linear matter perturbations, effectively distinguishing between models like wCDM and DGP by analyzing their growth factors across a range of redshifts.

Contribution

It proposes a novel form for the growth index b3(z) and demonstrates its accuracy and utility in differentiating cosmological models using observational data.

Findings

The proposed b3(z) form accurately approximates growth factors with errors below 0.03% for b4b1CDM.

b3_1 is negative for wCDM and positive for DGP, providing a signature to discriminate models.

The parametrization is effective across redshifts 0.15 to 3.8 for constraining growth indices.

Abstract

We propose a parametrization for the growth index of the linear matter perturbations, $\gamma(z)=\gamma_0+\frac{z}{1+z}\gamma_1$. The growth factor of the perturbations parameterized as $\Omega_m^{\gamma}$ is analyzed for both the $w$CDM model and the DGP model with our proposed form for $\gamma$. We find that $\gamma_1$ 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 $\Omega_m^{\gamma}$ with $\gamma$ 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 $\Lambda$CDM model and 0.18% for the DGP model for all redshifts when $\Omega_{m0}=0.27$. 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.