Dispersion in the growth of matter perturbations

TL;DR

This paper investigates how scale-dependent modifications to gravity affect the growth of matter perturbations at low redshifts, highlighting the potential for dispersion effects to reveal the critical scale of the fifth-force.

Contribution

It generalizes the growth parameter constraints to models with scale-dependent effective gravity, enabling scale measurements to infer the fifth-force range.

Findings

Dispersion in growth occurs only near the critical scale rac{rac{

Measurement of rac{0(k) and rac{0'(k) can reveal the fifth-force scale rac{_{c,0}

Results are consistent with previous f(R) model analyses.

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 ~ \lambda_{c,0}, the range of the fifth-force today. We generalize the constraint equation satisfied by the parameters \gamma_0(k) and \gamma'_0(k) \equiv \frac{d\gamma(z,k)}{dz}(z=0) to models with G_{eff,0}(k) \ne G. Measurement of \gamma_0(k) and \gamma'_0(k) on several scales can provide information about \lambda_{c,0}. In the absence of dispersion when \lambda_{c,0} is large compared to the probed scales, measurement of \gamma_0 and \gamma'_0 provides a consistency check independent of \lambda_{c,0}. This applies in particular to results obtained earlier for a viable f(R) model.