On the growth of linear perturbations

TL;DR

This paper investigates the growth of matter perturbations in dark energy models, establishing a constraint at zero redshift and analyzing the behavior of the growth index gamma and its derivative across different models.

Contribution

It derives a specific constraint linking background and dark energy parameters to matter perturbation growth, and characterizes the behavior of gamma' in various dark energy models within GR.

Findings

For DM, mma'0 is tightly constrained between -0.0195 and -0.0157.

Constant equation of state models have a nearly constant mma'0 around -0.02.

Varying equation of state models do not produce mma'0 with magnitude greater than 0.02.

Abstract

We consider the linear growth of matter perturbations in various dark energy (DE) models. We show the existence of a constraint valid at $z=0$ between the background and dark energy parameters and the matter perturbations growth parameters. For $\Lambda$CDM $\gamma'_0\equiv \frac{d\gamma}{dz}_0$ lies in a very narrow interval $-0.0195 \le \gamma'_0 \le -0.0157$ for $0.2 \le \Omega_{m,0}\le 0.35$. Models with a constant equation of state inside General Relativity (GR) are characterized by a quasi-constant $\gamma'_0$, for $\Omega_{m,0}=0.3$ for example we have $\gamma'_0\approx -0.02$ while $\gamma_0$ can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either $|\gamma'_0|>0.02$. A measurement of $\gamma(z)$ on small redshifts could help discriminate between various DE models even if their $\gamma_0$ is close, a possibility interesting for DE models outside GR for which a significant $\gamma'_0$ can be obtained.