Can observational growth rate data favour the clustering dark energy models?

Under the commonly used assumption that clumped objects can be well described by a spherical top-hat matter density profile, we investigate the evolution of the cosmic growth index in clustering dark energy (CDE) scenarios on sub-horizon scales. We show that the evolution of the growth index $\gamma (z)$ strongly depends on the equation-of-state (EoS) parameter and on the clustering properties of the dark energy (DE) component. Performing a ${\chi }^2$ analysis, we show that CDE models have a better fit to observational growth rate data points with respect to the concordance $\mathrm{\Lambda }$CDM model. We finally determine $\gamma (z)$ using an exponential parametrization and demonstrate that the growth index in CDE models presents large variations with cosmic redshift. In particular it is smaller (larger) than the theoretical value for the $\mathrm{\Lambda }$CDM model, ${\gamma }_{\mathrm{\Lambda }}\simeq 0.55$, in the recent past (at the present time).