The Homogeneity Scale of the universe
  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.
