English

On the growth of linear perturbations

Astrophysics 2008-11-26 v2 General Relativity and Quantum Cosmology

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=0z=0 between the background and dark energy parameters and the matter perturbations growth parameters. For Λ\LambdaCDM γ0dγdz0\gamma'_0\equiv \frac{d\gamma}{dz}_0 lies in a very narrow interval 0.0195γ00.0157-0.0195 \le \gamma'_0 \le -0.0157 for 0.2Ωm,00.350.2 \le \Omega_{m,0}\le 0.35. Models with a constant equation of state inside General Relativity (GR) are characterized by a quasi-constant γ0\gamma'_0, for Ωm,0=0.3\Omega_{m,0}=0.3 for example we have γ00.02\gamma'_0\approx -0.02 while γ0\gamma_0 can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either γ0>0.02|\gamma'_0|>0.02. A measurement of γ(z)\gamma(z) on small redshifts could help discriminate between various DE models even if their γ0\gamma_0 is close, a possibility interesting for DE models outside GR for which a significant γ0\gamma'_0 can be obtained.

Keywords

Cite

@article{arxiv.0710.1510,
  title  = {On the growth of linear perturbations},
  author = {David Polarski and Radouane Gannouji},
  journal= {arXiv preprint arXiv:0710.1510},
  year   = {2008}
}

Comments

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

R2 v1 2026-06-21T09:28:13.711Z