The growth of linear perturbations in the DGP model

TL;DR

This paper investigates the linear growth of matter perturbations in the DGP model, deriving the growth index as a function of redshift and comparing it with observational data to assess model viability.

Contribution

It introduces a parameterization of the growth index in the DGP model and constrains it using low redshift observational data, providing a comparison with the mbda CDM model.

Findings

The growth index mbda(z) is well approximated by a linear function of redshift.

Observations favor mbda CDM but are consistent with DGP at 1onfidence level.

Constraints on mbda and DGP models are derived from growth factor data.

Abstract

We study the linear growth of matter perturbations in the DGP model with the growth index $\gamma$ as a function of redshift. At the linear approximation: $\gamma(z)\approx\gamma_0+\gamma_0^\prime z $, we find that, for $0.2\leq\Omega_{m,0}\leq0.35$, $\gamma_0$ takes the value from 0.658 to 0.671, and $\gamma_0^\prime$ ranges from 0.035 to 0.042. With three low redshift observational data of the growth factor, we obtain the observational constraints on $\gamma_0$ and $\gamma_0'$ for the $\Lambda CDM$ and DGP models and find that the observations favor the $\Lambda CDM$ model but at the $1\sigma$ confidence level both the $\Lambda CDM$ and DGP models are consistent with the observations.