Resumen:
The standard model of cosmology is based on the Cosmological Principle (CP), which states that, on large scales, the Universe is homogeneous and isotropic. It predicts that the transition from an inhomogenous to a homogeous Universe is smooth. Today with the big and deep galaxy surveys mapping the luminous mass distribution of the Universe, we have the possibility to explore the CP. In a model independent analysis, this work study the transition to homogeneity in the local Universe ($ z<0.06 $) from a HI sample of the ALFALFA catalog. We used the scaled count-in-sphere, $ \mathcal{N}(<r) $ and the correlation dimension $ \mathcal{D}_{2}(r) $, adapted to the case of a projected analyses. The methodology employed has the advantage of using random catalogs that weight the geometric and incompleteness effects of the survey. We used three estimators to obtain $ \mathcal{N}(<\theta) $ and $ \mathcal{D}_{2}(\theta) $ to probe the transition to homogeneity, $ \theta_{H} $. Our analysis show a transition in a range $ 15.38º-16.49º $. Moreover, our approach is able to indicate the presence of under- and over-densities in the data, the latter possibly originated by a galaxy cluster. Robustness tests confirmed the validity of our metodology using fractal catalogs with a known dimension and geometry like ALFALFA sample.
