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We test the homogeneity of the Universe at z\ 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 R³ at radii greater than R\ 70 h^-1. 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 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 (\ 2\10⁷ h^-3 ³) regions is found to be 7 percent of the mean density. This variance is consistent with typical biased \ models and puts very strong constraints on the quality of SDSS photometric calibration.
Hogg et al. (Wed,) studied this question.