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

TL;DR

This paper introduces a new angular correlation dimension $D_2$ method that reduces nonlinear distortion effects, enabling robust, model-independent estimates of galaxy bias and matter density from galaxy surveys, consistent with CMB results.

Contribution

The paper presents a novel angular $D_2$ statistic that minimizes nonlinear distortion impacts, providing a robust, model-independent way to constrain cosmological parameters from galaxy data.

Findings

The $D_2$ method reduces systematic errors from Finger-of-God effects.

Robust estimates of $oldsymbol{ extomega_m}$ are obtained from SDSS data.

Results agree with current CMB 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 corresponds to comoving scales of $\sim 20\,h^{-1}\,\mathrm{Mpc}$ 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 $\omega_m = 0.142^{+0.014}_{-0.022}$ (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.