The impact of dark energy perturbations on the growth index

Abstract: We show that in clustering dark energy models the growth index of linear matter perturbations, $\gamma$, can be much lower than in $\Lambda$CDM or smooth quintessence models and present a strong variation with redshift. We find that the impact of dark energy perturbations on $\gamma$ is enhanced if the dark energy equation of state has a large and rapid decay at low redshift. We study four different models with these features and show that we may have $0.33<\gamma\left(z\right)<0.48$ at $0<z<3$. We also show that the constant $\gamma$ parametrization for the growth rate, $f=d\ln\delta_{m}/d\ln a=\Omega_{m}^{\gamma}$, is a few percent inaccurate for such models and that a redshift dependent parametrization for $\gamma$ can provide about four times more accurate fits for $f$. We discuss the robustness of the growth index to distinguish between General Relativity with clustering dark energy and modified gravity models, finding that some $f\left(R\right)$ and clustering dark energy models can present similar values for $\gamma$.