The homogeneity scale and the growth rate of cosmic structures

We propose a novel approach to obtain the growth rate of cosmic structures, f(z), from the evolution of the cosmic homogeneity scale, R-H(z). Ourmethodology needs two ingredients in a specific functional form: R-H(z) data and thematter two-point correlation function today, i.e. xi (r, z = 0). We use a Gaussian Process approach to reconstruct the function R-H. In the absence of suitable observational information of the matter correlation function in the local Universe, z similar or equal to 0, we assume a fiducial cosmology to obtain. (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(RH) (z) obtained through our approach, (ii) the f(Lambda CDM)(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 f(data)(z) and compare it with the function f(RH)(z) finding a concordance of < 2 sigma, a good result considering the few data available for both reconstruction processes. With more accurate R-H(z) data, from forthcoming surveys, the homogeneity scale function might be better determined and would have the potential to discriminate between Lambda CDM and alternative scenarios as a new cosmological observable.

Automated summary

The study presents a novel approach to obtaining the growth rate of cosmic structures from the evolution of the cosmic homogeneity scale. The results show consistency between the growth rate obtained through the proposed approach, the expected growth rate in the standard model, and the best-fitting growth rate from existing data.