The scale of homogeneity in the local Universe with the ALFALFA catalogue

We use the scaled counts in spherical caps $mathcal{N}(<theta)$ and the fractal correlation dimension $ mathcal{D}_{2}(theta) $ procedures to search for a transition scale to homogeneity in the local universe as given by the ALFALFA catalogue (a sample of extragalactic HI line sources, in the redshift range $0 < z < 0.06$). Our analyses, in the 2-dimensional sky projected data, show a transition to homogeneity at $theta_H = 16.49^{circ} pm 0.29^{circ}$, in remarkable accordance with the angular scale expected from simulations, a result that strengthens the validity of the cosmological principle in the local universe. We test the robustness of our results by analysing the data sample using thr