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 4 redshift bins, each one with $N_{\rm q} \geq 19,000$ 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, $D_2$. Using the $\Lambda$CDM cosmology as the fiducial model, we first estimate the redshift evolution of quasar bias and then the homogeneity scale of the underlying matter distribution $r_{\rm{hom}}^{\rm{m}}$. We find that $r_{\rm{hom}}^{\rm{m}}$ exhibits a decreasing trend with redshift and that the values obtained are in good agreement with the $\Lambda$CDM 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