Dispersion in the growth of matter perturbations

Abstract

We consider the linear growth of matter perturbations on low redshifts in modified gravity Dark Energy (DE) models where G_eff(z,k) is explicitly scale-dependent. Dispersion in the growth today will only appear for scales of the order the critical scale ~ λ_{c,0}, the range of the fifth-force today. We generalize the constraint equation satisfied by the parameters γ_0(k) and γ'_0(k) \equiv \frac{dγ(z,k)}{dz}(z=0) to models with G_{eff,0}(k) \ne G. Measurement of γ_0(k) and γ'_0(k) on several scales can provide information about λ_{c,0}. In the absence of dispersion when λ_{c,0} is large compared to the probed scales, measurement of γ_0 and γ'_0 provides a consistency check independent of λ_{c,0}. This applies in particular to results obtained earlier for a viable f(R) model.

8 pages, 5 figures