The homogeneity scale and the growth rate of cosmic structures

TL;DR

This paper introduces a new method to determine the growth rate of cosmic structures using the evolution of the cosmic homogeneity scale, combining Gaussian Process reconstruction with existing data to test cosmological models.

Contribution

It proposes a novel approach linking the homogeneity scale evolution to the growth rate, providing a new cosmological observable for model testing.

Findings

Good agreement between the reconstructed growth rate and the fiducial $ m extLambda$CDM model.

The reconstructed growth rate from data aligns within 2 sigma with the homogeneity scale method.

Potential for future surveys to improve constraints and discriminate between cosmological models.

Abstract

We propose a novel approach to obtain the growth rate of cosmic structures, $f(z)$, from the evolution of the cosmic homogeneity scale, $R_{\text{H}}(z)$. Our methodology needs two ingredients in a specific functional form: $R_{\text{H}}(z)$ data and the matter two-point correlation function today, i.e., $\xi(r, z=0)$. We use a Gaussian Process approach to reconstruct the function $R_{\text{H}}$. In the absence of suitable observational information of the matter correlation function in the local Universe, $z \simeq 0$, we assume a fiducial cosmology to obtain $\xi(r, z=0)$. 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 $f^{\Lambda\text{CDM}}(z)$ expected in the fiducial model, and (iii) the best-fit $f(z)$ from data compiled in the literature. Moreover, using this data compilation, we perform a Gaussian Process to reconstruct the growth rate function $f^{\text{data}}(z)$ and compare it with the function $f^{R_{\text{H}}}(z)$ finding a concordance of $< \!2 \,\sigma$, a good result considering the few data available for both reconstruction processes. With more accurate $R_{\text{H}}(z)$ 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.