We test the homogeneity of the Universe at z \sim 0.3 with the Luminous Red Galaxy ( LRG ) spectroscopic sample of the Sloan Digital Sky Survey .
First , the mean number N ( R ) of LRGs within completely surveyed LRG-centered spheres of comoving radius R is shown to be proportional to R ^ { 3 } at radii greater than R \sim 70 h ^ { -1 } ~ { } \mathrm { Mpc } .
The test has the virtue that it does not rely on the assumption that the LRG sample has a finite mean density ; its results show , however , that there is such a mean density .
Secondly , the survey sky area is divided into 10 disjoint solid angular regions and the fractional rms density variations of the LRG sample in the redshift range 0.2 < z < 0.35 among these ( \sim 2 \times 10 ^ { 7 } h ^ { -3 } ~ { } \mathrm { Mpc ^ { 3 } } ) regions is found to be 7 percent of the mean density .
This variance is consistent with typical biased \Lambda CDM models and puts very strong constraints on the quality of SDSS photometric calibration .