Cosmic homogeneity: the effect of redshift-space distortions and bias and cosmological constraints

Abstract

We present a novel cosmological analysis based on the angular correlation dimension $D_2$ curve, a cumulative statistic derived from the two-point correlation function. Unlike traditional 3D approaches, angular $D_2$ is inherently less sensitive to nonlinear dynamical distortions, such as the small-scale Finger-of-God (FoG) effect. Using both MultiDark-Patchy and EZmock galaxy catalogs, we assess the scale-dependent impact of redshift-space distortions on $D_2$ and bias measurements. We demonstrate that the systematic errors associated with FoG modeling can be significantly reduced by restricting the analysis to appropriate minimum comoving angular scales of $\sim 1.25^{\circ }$, which corresponding to physical scales of $18$-$23h^{-1}\mathrm{Mpc}$ over the redshift range $0.46\le z\le 0.74$ within the standard $\Lambda$CDM model. Since the observational estimative of $D_2(\theta )$ is not dependent on a cosmological model we obtain robust estimates of the galaxy bias and place competitive constraints on the physical matter density ${\omega }_m$. By applying this framework to SDSS DR12 and DR16 Luminous Red Galaxy data, we obtain ${\omega }_m=0.137_{-0.059}^{+0.041}$ (1$\sigma$), which agrees with current CMB analyses. Our results highlight the potential of the angular $D_2$ curve as a model-independent and robust tool for cosmological parameter inference.