Exploring cosmic homogeneity with the BOSS DR12 galaxy sample

In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, 3 h-3 Gpc3 at 0.43 ≤ z ≤ 0.7. We study the scaled counts-in-spheres, N(<r), and the fractal correlation dimension, D2(r), to assess the homogeneity scale of the universe using a Landy & Szalay inspired estimator. Defining the scale of transition to homogeneity as the scale at which D2(r) reaches 3 within 1%, i.e. D2(r)>2.97 for r>RH, we find RH = (63.3±0.7) h-1 Mpc, in agreement at the percentage level with the predictions of the ΛCDM model RH=62.0 h-1 Mpc. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the ΛCDM prediction. Finally, we find that 2 is compatible with 3 at scales larger than 300 h-1 Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the ΛCDM model