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 ∼ 1.25°, which corresponding to physical scales of 18–23 h -1 Mpc over the redshift range 0.46 ≤ z ≤ 0.74 within the standard ΛCDM model. Since the observational estimative of D 2 ( θ ) is not dependent on a cosmological model we obtain robust estimates of the galaxy bias and place competitive constraints on the physical matter density ω m . By applying this framework to SDSS DR12 and DR16 Luminous Red Galaxy data, we obtain ω m = 0.137 +0.041 -0.059 (1 σ ), 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.