Abstract:
We investigate the transition scale to homogeneity, RH , using as cosmic tracer the spectroscopic sample of blue galaxies from the Sloan Digital Sky Survey (SDSS). Considering the spatial distribution of the galaxy sample, we compute the two point correlation function, ξ(r), the scaled counts in spheres, N (< r), and the fractal dimension, D2(< r), to quantify the homogeneity scale in the Local Universe (0.04 < z < 0.20). The sample in analysis is compared with random and mock catalogues with the same geometry, and the same density as the dataset, to calculate the covariance matrix for the errors determination. The criteria adopted for the transition-to-homogeneity follows the literature, it is attained when D2(< r) reaches the 1% level of the limit value 3 (i.e., where it reaches 2.97) as the scale increases. We obtain RH = 70.00 ± 9.26 M pc/h, at the effective redshift z_ef = 0.128, for a sample containing 150 302 SDSS blue galaxies with 0.04 < z < 0.20. Additionally, we perform robustness tests by analyzing the homogeneity scale in sub-volumes of the original one, obtaining coherent results; we also check for a possible artifact in our procedure examining a homogeneous synthetic dataset as a pseudo-data, verifying that such systematic is absent. Because our analyses concentrate in data at low redshifts, z < 0.20, we find interesting to use cosmography to calculate the radial comoving distances; therefore in this subject our analyses do not use fiducial cosmological model. For completeness, we evaluate the difference of the comoving distances estimation using cosmography and fiducial cosmology.
