We present the large-scale correlation function measured from a spectroscopic sample of 46,748 luminous red galaxies from the Sloan Digital Sky Survey. The survey region covers 0.72h−3Gpc3 over 3816 square degrees and 0.16 < z < 0.47, making it the best sample yet for the study of large-scale structure. We find a well-detected peak in the correlation function at 100h−1Mpc separation that is an excellent match to the predicted shape and location of the imprint of the recombination-epoch acoustic oscillations on the low-redshift clustering of matter. This detection demonstrates the linear growth of structure by gravitational instability between z ≈ 1000 and the present and confirms a firm prediction of the standard cosmological theory. The acoustic peak provides a standard ruler by which we can measure the ratio of the distances to z = 0.35 and z = 1089 to 4% fractional accuracy and the absolute distance to z = 0.35 to 5% accuracy. From the overall shape of the correlation function, we measure the matter density mh2 to 8% and find agreement with the value from cosmic microwave background (CMB) anisotropies. Independent of the constraints provided by the CMB acoustic scale, we find m = 0.273±0.025+0.123(1+w0)+0.137 K. Including the CMB acoustic scale, we find that the spatial curvature is K = −0.010± 0.009 if the dark energy is a cosmological constant. More generally, our results provide a measurement of cosmological distance, and hence an argument for dark energy, based on a geometric method with the same simple physics as the microwave background anisotropies. The standard cosmological model convincingly passes these new and robust tests of its fundamental properties. (Refer to PDF file for exact formulas).

Publication Date



This is the pre-print of an article published by the American Astronomical Society. The final, published version is available here: https://doi.org/10.1086/466512

© 2005 The American Astronomical Society

Also archived in: arXiv:astro-ph/0501171 v1 10 Jan 2005

DJE, IZ, and HS are supported by grant AST-0098577 and AST-0407200 from the National Science Foundation. DJE is further supported by an Alfred P. Sloan Research Fellowship. DWH and MRB were supported by NSF PHY-0101738 and NASA NAG5-11669. Our PTHalos mock catalogs were created on the NYU Beowulf cluster supported by NSF grant PHY-0116590. Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society.

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Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus