On the growth of linear perturbations

• DOI: 10.1016/j.physletb.2008.01.032
• Publication Date: 2008-01-31T16:08:16Z
• Authors: David Polarski; Radouane Gannouji
• Keywords: 04.62.+v; Nuclear and High Energy Physics; [SDU.ASTR]Sciences of the Universe [physics]/Astrophysics [astro-ph]; 98.80.Cq; Astrophysics (astro-ph); FOS: Physical sciences; General Relativity and Quantum Cosmology (gr-qc); Astrophysics; 01 natural sciences; General Relativity and Quantum Cosmology; 510; [PHYS.ASTR.CO]Physics [physics]/Astrophysics [astro-ph]/Cosmology and Extra-Galactic Astrophysics [astro-ph.CO]; 0103 physical sciences

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 $��$CDM $��'_0\equiv \frac{d��}{dz}_0$ lies in a very narrow interval $-0.0195 \le ��'_0 \le -0.0157$ for $0.2 \le ��_{m,0}\le 0.35$. Models with a constant equation of state inside General Relativity (GR) are characterized by a quasi-constant $��'_0$, for $��_{m,0}=0.3$ for example we have $��'_0\approx -0.02$ while $��_0$ can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either $|��'_0|>0.02$. A measurement of $��(z)$ on small redshifts could help discriminate between various DE models even if their $��_0$ is close, a possibility interesting for DE models outside GR for which a significant $��'_0$ can be obtained.<br/>8 pages, 8 figures. Results unchanged; clarifying sentence added; one reference added<br/>