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

TL;DR

This work investigates whether the angular homogeneity scale $\theta_H$ can serve as a model-independent cosmological test within a spatially flat $\Lambda$CDM framework. By relating the 2D fractal dimension $D_2(\theta)$ to the angular correlation function $\omega(\theta)$ via the Limber projection and a linear $\xi(r)$ computed from the matter power spectrum $P(k)$ (via CAMB), the authors derive theoretical predictions for $\theta_H$ and contrast them with the 3D counterpart $R_H$. They show that for $z \gtrsim 0.6$, $\theta_H$ exhibits a monotonic and sizable dependence on the matter density $\Omega_{\rm m0}$ and, crucially, on the Hubble constant $H_0$ (via $h$), making $\theta_H$ a potential probe of $H_0$ with reduced model dependence. Using three $\theta_H(z)$ measurements from eBOSS/DR16, they obtain $h = 0.642^{+0.068}_{-0.22}$ at 1$\sigma$, illustrating the method’s capability to constrain $h$ and suggesting that combining $\theta_H$ with BAO and other probes could help break parameter degeneracies and address tensions in the standard cosmology.

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 ($θ_H$) homogeneity scales with redshift, assuming a spatially flat, $Λ$-Cold Dark Matter %($Λ$CDM) universe and linear cosmological perturbation theory. We confirm previous results concerning the non-monotonicity of ${\cal{R}}_H$ with the matter density parameter $Ω_{m0}$ 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 $Ω_{m0}$ and $H_0$ but is quite sensitive to $H_0$, especially at higher redshifts. These results, therefore, raise the possibility of using $θ_H$ as a new, model-independent way to constrain cosmological parameters.

Figures (8)

• Figure 1: An illustration of the two-dimension shell where the 2PACF is computed. Angular: RA(degrees), Radial: redshift. a and b are the inner and outer radius of the spherical shell.
• Figure 2: The 3D fractal dimension $D_{2}(r)$ (left) and the 2D fractal dimension $D_{2}(\theta)$ (right) for selected values of $z$ assuming $\Omega_{\rm m0}=0.31$ and $H_{0}=67.66$. The dashed line corresponds to $1\%$ deviation from homogeneity for both cases, i.e., $D_{2}=2.97$ and $D_{2}=1.98$, respectively.
• Figure 3: The 3D homogeneity scale $R_{\rm H}$ as a function of the present matter density $\Omega_{\rm m0}$ for $h \in [0.4,1.0]$ at $z=0.4$, $0.64$, $3.0$. The 3D homogeneity scale $R_{\rm H}$ doesn't exhibit a monotonical behavior for all values of $\Omega_{\rm m0}$ in the range considered. The sudden change in $R_{\rm H}$ around $\Omega_{\rm m0}$=0.2 is due to the BAO feature results in a non-smooth behavior of homogeneity scale ntelis2019cosmological.
• Figure 4: The 3D homogeneity scale $R_{\rm H}$ as a function of the Hubble Constant $h$ for $\Omega_{\rm m0} \in [0.15,0.8]$ at $z=0.4$, $0.64$, $3.0$. The 3D homogeneity scale $R_{\rm H}$ exhibits a monotonically increasing behavior for all values of $h$ in the range considered.
• Figure 5: The angular homogeneity scale $\theta_H$ as a function of the present-day matter density parameter $\Omega_{m0}$ for the Hubble Constant $h \in [0.4,1.0]$ at $z=0.4$, $0.64$, $3.0$. We can see that $\theta_H$ is a monotonically increasing function for all values of $\Omega_{\rm m0}$ for $z \geq 0.64$.