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

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 ( RH R H ) and angular ( θ H θ H ) homogeneity scales with redshift, assuming a spatially flat, Λ -Cold Dark Matter universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of RH R H with the matter density parameter ₘ₀ Ω m0 but also show that it exhibits a monotonical behavior with the Hubble constant H₀ H 0 within a large redshift interval. More importantly, we find that, for z 0.6 z ≳ 0.6 , θ H θ H presents a monotonical behavior with ₘ₀ Ω m0 , as well as for H₀ H 0 the entire redshift interval analyzed. We find also that the angular homogeneity scale is sensitive to H₀ H 0 , especially at higher redshifts. Using the currently available θ H θ H measurements, we illustrate the constraints on the ₘ₀ Ω m0 – H₀ H 0 plane through a MCMC analysis and show the feasibility of using the angular homogeneity scale as a new, model-independent way to constrain cosmological parameters.