Cosmic homogeneity demonstrated with luminous red galaxies

Abstract

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 $R\sim 70h^{-1}\mathrm{Mpc}$. 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 \emph{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 ($\sim 2\times 10^7{h}^{-3}\mathrm{Mp}{\mathrm{c}}^3$) regions is found to be 7 percent of the mean density. This variance is consistent with typical biased \lcdm models and puts very strong constraints on the quality of SDSS photometric calibration.

arXiv commentsubmitted to ApJ

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