The Homogeneity Scale of the universe

Abstract: In this study, we probe the cosmic homogeneity with the BOSS CMASS galaxy sample in the redshift region of $0.43 < z < 0.7$. We use the normalised counts-in-spheres estimator $\mathcal{N}(<r)$ and the fractal correlation dimension $\mathcal{D}{2}(r)$ to assess the homogeneity scale of the universe. We verify that the universe becomes homogenous on scales greater than $\mathcal{R}{H} \simeq 64.3\pm1.6\ h^{-1}Mpc$, consolidating the Cosmological Principle with a consistency test of $\Lambda$CDM model at the percentage level. Finally, we explore the evolution of the homogeneity scale in redshift.