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

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 (${\mathcal{R}}_H$) 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 ${\mathcal{R}}_H$ 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.

arXiv comment10 pages, 24 figures

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