On the growth of linear perturbations

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 ${\gamma }_0^{\prime }\equiv {\frac{d\gamma }{dz}}_0$ lies in a very narrow interval $-0.0195\le {\gamma }_0^{\prime }\le -0.0157$ 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 ${\gamma }_0^{\prime }$, for ${\Omega }_{m,0}=0.3$ for example we have ${\gamma }_0^{\prime }\approx -0.02$ while ${\gamma }_0$ can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either $|{\gamma }_0^{\prime }|>0.02$. 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 ${\gamma }_0^{\prime }$ can be obtained.

8 pages, 8 figures. Results unchanged; clarifying sentence added; one reference added

References in corpus (1)

• Dark Energy versus Modified Gravity

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• Growth Index of DGP Model and Current Growth Rate Data
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• Probing the nature of cosmic acceleration