Precision growth index using the clustering of cosmic structures and growth data

Abstract: We use the clustering properties of Luminous Red Galaxies (LRGs) and the growth rate data provided by the various galaxy surveys in order to constrain the growth index ($\gamma$) of the linear matter fluctuations. We perform a standard $\chi^2$-minimization procedure between theoretical expectations and data, followed by a joint likelihood analysis and we find a value of $\gamma=0.56\pm 0.05$, perfectly consistent with the expectations of the $\Lambda$CDM model, and $\Omega_{m0} =0.29\pm 0.01$, in very good agreement with the latest Planck results. Our analysis provides significantly more stringent growth index constraints with respect to previous studies, as indicated by the fact that the corresponding uncertainty is only $\sim 0.09 \gamma$. Finally, allowing $\gamma$ to vary with redshift in two manners (Taylor expansion around $z=0$, and Taylor expansion around the scale factor), we find that the combined statistical analysis between our clustering and literature growth data alleviates the degeneracy and obtain more stringent constraints with respect to other recent studies.