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 0.72 h-3 Gpc3 over 3816 deg2 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 100 h-1 Mpc 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 Ωmh2 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 Ωm = 0.273 ± 0.025 + 0.123(1 + w0) + 0.137ΩK. Including the CMB acoustic scale, we find that the spatial curvature is ΩK = -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.

Detection of the Baryon Acoustic Peak in the Large‐Scale Correlation Function of SDSS Luminous Red Galaxies