Testing homogeneity in the Sloan Digital Sky Survey Data Release Twelve with Shannon entropy

Abstract

We analyse a set of volume-limited samples from SDSS DR12 to quantify the degree of inhomogeneity at different length-scales using Shannon entropy. We find that the galaxy distributions exhibit a higher degree of inhomogeneity as compared to a Poisson point process at all length-scales. Our analysis indicates that signatures of inhomogeneities in the galaxy distributions persist at least up to a length-scale of 120 h-1 Mpc. The galaxy distributions appear to be homogeneous on a scale of 140 h-1 Mpc and beyond. Analysing a set of mock galaxy samples from a semi-analytic galaxy catalogue from the Millennium simulation, we find a scale of transition to homogeneity at ~100 h-1 Mpc.