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) Gpc~3 over 3816 deg~2 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 Ω_mh~2 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 Ω_m = 0.273 ± 0.025 + 0.123(1 + w_0) + 0.137Ω_K. Including the CMB acoustic scale, we find that the spatial curvature is Ω_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.
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