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 γ) of the linear matter fluctuations. We perform a standard χ2-minimization procedure between theoretical expectations and data, followed by a joint likelihood analysis and we find a value of γ=0.56± 0.05, perfectly consistent with the expectations of the ΛCDM model, and Ωm0 =0.29± 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 ~ 0.09 γ. Finally, allowing γ 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.



v ~ 6 × 1012 h
M☉,
v ~ 0.4 h
, where γ ≡ γ(Ωm, w), and it is valid for all w < –
models. By combining the X-ray clustering and SN Ia data we find that the model that best reproduces the observational data is that with Ωm
arcsec and γ = 2.2 ± 0.30. Fixing the correlation function slope to γ = 1.8, we obtain θ0 = 22.2
arcsec. Using Limber’s integral equation and a variety of possible luminosity functions of the hard X-ray population, we find a relatively large correlation length, ranging from r0 ~ 9 to 19 h-1 Mpc (for γ = 1.8 and the concordance cosmological model), with this range reflecting also different evolutionary models for the source luminosities and clustering characteristics. The relatively large correlation length is comparable to that of extremely red objects and luminous radio sources.





.