Euclid: Homogeneity in the search of the Dark Sector

In the era of precision cosmology, we investigate an novel method to probe the Dark Universe. By studying the fractality of the universe, we estimate a characteristic scale of homogeneity. Using the Flagship representative catalogue of Euclid Mission at an effective redshift $z_{eff} = 1.15$, we measure this scale $R_H = 85\pm 1 h^{-1}$Mpc at %-level, consistent at $1\sigma$ with the theoretical prediction, i.e. $R_H^{th} = 86 h^{-1}$Mpc. We have shown with a Fisher analysis that the homogeneity scale is a complementary cosmological probe which will help us understand the nature of Dark Energy and Dark Matter of our universe.