Measuring the scale of cosmic homogeneity with SDSS-IV DR14 quasars

The quasar sample of the fourteenth data release of the Sloan Digital Sky Survey (SDSS-IV DR14) is used to determine the cosmic homogeneity scale in the redshift range 0. 80 < |z| < 2. 24. We divide the sample into four redshift bins, each one with |N ₐ 19\, 000| quasars, spanning the whole redshift coverage of the survey and use two correlation function estimators to measure the scaled counts-in-spheres and its logarithmic derivative, i. e. the fractal correlation dimension, D2. Using the ΛCDM cosmology as the fiducial model, we first estimate the redshift evolution of quasar bias and then the homogeneity scale of the underlying matter distribution |r ₇₎₌^ {m}|⁠. We find that |r ₇₎₌^ {m}| exhibits a decreasing trend with redshift and that the values obtained are in good agreement with the ΛCDM prediction over the entire redshift interval studied. We, therefore, conclude that the large-scale homogeneity assumption is consistent with the largest spatial distribution of quasars currently available.