  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 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^{-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 Omega_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 Omega_m = 0.273
+- 0.025 + 0.123 (1+w_0) + 0.137 Omega_K. Including the CMB acoustic scale, we
find that the spatial curvature is Omega_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.
