Can the angular scale of cosmic homogeneity be used as a cosmological test?

TL;DR

This paper investigates the evolution of cosmic homogeneity scales with redshift in a flat $ m{ extLambda}$CDM universe, highlighting the potential of the angular scale as a new cosmological parameter constraint method.

Contribution

It extends previous studies by analyzing the redshift evolution of spatial and angular homogeneity scales, emphasizing the sensitivity of the angular scale to cosmological parameters at high redshift.

Findings

The spatial homogeneity scale ${ m{ extR}}_H$ shows non-monotonic behavior with $ m{ extOmega}_{m0}$.

The angular homogeneity scale $ heta_H$ is sensitive to $H_0$ at $z ightarrow 0.6$ and above.

$ heta_H$ exhibits a monotonic relation with $ m{ extOmega}_{m0}$ and $H_0$ at higher redshifts.

Abstract

In standard cosmology, the cosmic homogeneity scale is the transition scale above which the patterns arising from non-uniformities -- such as groups and clusters of galaxies, voids, and filaments -- become indistinguishable from a random distribution of sources. Recently, different groups have investigated the feasibility of using such a scale as a cosmological test and arrived at different conclusions. In this paper, we complement and extend these studies by exploring the evolution of the spatial (${\cal{R}}_H$) and angular ($\theta_H$) homogeneity scales with redshift, assuming a spatially flat, $\Lambda$-Cold Dark Matter %($\Lambda$CDM) universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of ${\cal{R}}_H$ with the matter density parameter $\Omega_{m0}$ but also show that it exhibits a monotonical behavior with the Hubble constant $H_0$ within a large redshift interval. More importantly, we find that, for $z \gtrsim 0.6$, the angular homogeneity scale not only presents a monotonical behavior with $\Omega_{m0}$ and $H_0$ but is quite sensitive to $H_0$, especially at higher redshifts. These results, therefore, raise the possibility of using $\theta_H$ as a new, model-independent way to constrain cosmological parameters.