ANALYSIS OF THE STATISTICAL ISOTROPY IN THE DISTRIBUTION OF STRUCTURES IN THE LOCAL UNIVERSE

Abstract

We investigate the statistical isotropy of the Local Universe by employing model- independent analyses using the Arecibo Legacy FAST Alfa Survey (ALFALFA) data, which covers a redshift range of 0 < z < 0.06. The flat-ΛCDM model currently exhibits the best agreement with observational data obtained from various cosmic tracers. This model is based on the Cosmological Principle, which assumes statistical homogeneity (invariance under translation) and isotropy (invariance under rotation) on large scales. Our analysis specifically examines the issue of isotropy by exploring the directional characteristics of the Local Universe through the ALFALFA catalog. This catalog encompasses 7000 deg2 of the sky and includes 31502 extragalactic HI sources divided between the northern and southern Galactic hemispheres. While numerous isotropy analyses have been conducted using cosmic microwave background radiation (CMB) data at z = 1100, only a few studies have employed galaxy catalogs, particularly at low redshifts (z < 0.06). Our preliminary findings suggest that the Local Universe is statistically isotropic. However, our analysis reveals the presence of significant underdensities in certain regions, particularly in proximity to the Local Cosmic Void, which was initially described by Tully & Fisher (1987). To assess isotropy, we utilized the two-point angular correlation function, employing the Landy-Szalay estimator as statistical measure. Additionally, we employed log-normal simulations (which consider the best Planck’s cosmological parameters) to estimate uncertainties. To gain insight into the properties and morphology of the examined structure, we determined the parameters θ0 (the transition scale between nonlinear and linear regimes) and β (which quantifies matter clustering) at small and large scales. Furthermore, we evaluated the statistical significance of our results, conducted complementary tests using simulated voids, and performed comparative investigations by referring to existing liter- ature on voids in the Local Universe. Our findings indicate that, apart from the Local Cosmic Void (with a number-density contrast of δ = -0.7), the region covered by the ALFALFA survey also encompasses partially other underdense regions or voids, including the Dipole Repeller.