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 $\gamma$.

7 pages, 6 figures, minor changes, matches the accepted version in Phys. Rev. D

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• Growth index and statefinder diagnostic of Oscillating Dark Energy
• Observational constraints on Starobinsky $f(R)$ cosmology from cosmic expansion and structure growth data
• Growth of matter perturbations in the extended viscous dark energy models
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• Scalar field descriptions of two dark energy models
• Non-linear dark matter collapse under diffusion
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• Can dark energy explain a high growth index?
• Scalar perturbation and density contrast evolution in $f(Q,C)$ gravity