On the growth of linear perturbations

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)' d gamma/dz vertical bar(0) lies in a very narrow interval -0.0195 <= gamma(0)' <= -0.0157 for 0.2 <= Omega(m,0) <= 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)' approximate to -0.02 while gamma(0) can have a nonnegligible variation. A smoothly varying equation of state inside GR does not produce either vertical bar gamma(0)'vertical bar > 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. (c) 2008 Elsevier B.V. All rights reserved.