No abstract

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 −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 Ω m h 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. Subject headings: cosmology: observations -large-scale structure of the universe -distance scalecosmological parameters -cosmic microwave background -galaxies: elliptical and lenticular, cD

We measure cosmological parameters using the three-dimensional power spectrum P (k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a "vanilla" flat adiabatic ΛCDM model without tilt (ns = 1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1σ constraints on the Hubble parameter from h ≈ 0.74−0.03 , on the matter density from Ωm ≈ 0.25 ± 0.10 to Ωm ≈ 0.30 ± 0.04 (1σ) and on neutrino masses from < 11 eV to < 0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0 ≈ 16.3 +2.3 −1.8 Gyr to t0 ≈ 14.1Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.

Using a catalog of 147,986 galaxy redshifts and fluxes from the Sloan Digital Sky Survey (SDSS), we measure the galaxy luminosity density at z ¼ 0:1 in five optical bandpasses corresponding to the SDSS bandpasses shifted to match their rest-frame shape at z ¼ 0:1. We denote the bands 0.1 u, 0.1 g, 0.1 r, 0.1 i, 0.1 z with eff ¼ ð3216; 4240; 5595; 6792; 8111 GÞ, respectively. To estimate the luminosity function, we use a maximum likelihood method that allows for a general form for the shape of the luminosity function, fits for simple luminosity and number evolution, incorporates the flux uncertainties, and accounts for the flux limits of the survey. We find luminosity densities at z ¼ 0:1 expressed in absolute AB magnitudes in a Mpc 3 to be (À14:10 AE 0:15, À15:18 AE 0:03, À15:90 AE 0:03, À16:24 AE 0:03, À16:56 AE 0:02) in ( 0.1 u, 0.1 g, 0.1 r, 0.1 i, 0.1 z), respectively, for a cosmological model with 0 ¼ 0:3, à ¼ 0:7, and h ¼ 1 and using SDSS Petrosian magnitudes. Similar results are obtained using Sérsic model magnitudes, suggesting that flux from outside the Petrosian apertures is not a major correction. In the 0.1 r band, the best-fit Schechter function to our results has à ¼ ð1:49 AE 0:04Þ Â 10 À2 h 3 Mpc À3 , M à À 5 log 10 h ¼ À20:44 AE 0:01, and ¼ À1:05 AE 0:01. In solar luminosities, the luminosity density in 0.1 r is ð1:84 AE 0:04Þ Â 10 8 h L 0:1 r; Mpc À3 . Our results in the 0.1 g band are consistent with other estimates of the luminosity density, from the Two-Degree Field Galaxy Redshift Survey and the Millennium Galaxy Catalog. They represent a substantial change ($0.5 mag) from earlier SDSS luminosity density results based on commissioning data, almost entirely because of the inclusion of evolution in the luminosity function model.