Abstract

We consider the linear growth of matter perturbations on low redshifts in some f(R) dark energy (DE) models. We discuss the definition of dark energy (DE) in these models and show the differences with scalar-tensor DE models. For the f(R) model recently proposed by Starobinsky we show that the growth parameter γ 0≡γ(z = 0) takes the value γ 0 0.4 for Ω m,0 = 0.32 and γ 0 0.43 for Ω m,0 = 0.23, allowing for a clear distinction from ΛCDM. Though a scale-dependence appears in the growth of perturbations on higher redshifts, we find no dispersion for γ(z) on low redshifts up to z ∼ 0.3, γ(z) is also quasi-linear in this interval. At redshift z = 0.5, the dispersion is still small with Δγ 0.01. As for some scalar-tensor models, we find here too a large value for γ′ 0≡(dγ/dz)(z = 0), γ′ 0 -0.25 for Ω m,0 = 0.32 and γ′ 0 -0.18 for Ω m,0 = 0.23. These values are largely outside the range found for DE models in General Relativity (GR). This clear signature provides a powerful constraint on these models.