The homogeneity scale and the growth rate of cosmic structures

Abstract

ABSTRACT We propose a novel approach to obtain the growth rate of cosmic structures, f(z), from the evolution of the cosmic homogeneity scale, RH(z). Our methodology needs two ingredients in a specific functional form: RH(z) data and the matter two-point correlation function today, i.e. ξ(r, z = 0). We use a Gaussian Process approach to reconstruct the function RH. In the absence of suitable observational information of the matter correlation function in the local Universe, z ≃ 0, we assume a fiducial cosmology to obtain ξ(r, z = 0). For this reason, our final result turns out to be a consistency test of the cosmological model assumed. Our results show a good agreement between: (i) the growth rate $f^{R_{\text{H}}}(z)$ obtained through our approach, (ii) the fΛCDM(z) expected in the fiducial model, and (iii) the best-fitting f(z) from data compiled in the literature. Moreover, using this data compilation, we perform a Gaussian Process to reconstruct the growth rate function fdata(z) and compare it with the function $f^{R_{\text{H}}}(z)$ finding a concordance of $\lt \!2 \, \sigma$, a good result considering the few data available for both reconstruction processes. With more accurate RH(z) data, from forthcoming surveys, the homogeneity scale function might be better determined and would have the potential to discriminate between ΛCDM and alternative scenarios as a new cosmological observable.