Do we live in an under-dense region?

Abstract

According to the Cosmological Principle, matter structures and radiation are expected to be homogeneously and isotropically distributed in the universe at sufficiently large scales. An open question in observational cosmology is to estimate the size of such scale from the data. In the case of the cosmic background radiation, it seems clear that such scale corresponds to the horizon scale at matter-radiation decoupling, that is, at ∼ 1°, but the problem is still open for the size of the homogeneity scale. But, due to the growth of structures in the evolving universe the homogeneity scale depends on the redshift of the data in analyses. Here we study this problem for data in the local universe by analyzing the 21cm HI-line sources using the public catalog ALFALFA, with median redshift 〈z〉 = 0.025. We use the scaled counts-in-spheres method to establish the approximate size of the homogeneity scale in the local universe. In this analysis one compares the data sample with respect to a randomly generated homogenous sample. Defining the scale of transition to homogeneity as the scale at which the scaled counts-in-spheres estimator reaches the limiting value 1 within 1%, we find that this transition scale is rH ≃ 69 Mpc, in excellent accordance with what is expected considering that the HI-line sources come from low-mass blue galaxies which have an anti-bias b with respect to the matter fluctuation field (with b ≃ 0.48 − 0.68 depending on the composition of the sample), from which one expects a transition scale in the local universe of 56 < rH < 79 Mpc.