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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.

We measure the large-scale real-space power spectrum P (k) using a sample of 205,443 galaxies from the Sloan Digital Sky Survey, covering 2417 effective square degrees with mean redshift z ≈ 0.1. We employ a matrix-based method using pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimumvariance measurements in 22 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.02 h/Mpc < k < 0.3 h/Mpc. We pay particular attention to modeling, quantifying and correcting for potential systematic errors, nonlinear redshift distortions and the artificial red-tilt caused by luminosity-dependent bias. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. Our final result is a measurement of the real-space matter power spectrum P (k) up to an unknown overall multiplicative bias factor. Our calculations suggest that this bias factor is independent of scale to better than a few percent for k < 0.1 h/Mpc, thereby making our results useful for precision measurements of cosmological parameters in conjunction with data from other experiments such as the WMAP satellite. The power spectrum is not well-characterized by a single power law, but unambiguously shows curvature. As a simple characterization of the data, our measurements are well fit by a flat scaleinvariant adiabatic cosmological model with hΩ m = 0.213 ± 0.023 and σ 8 = 0.89 ± 0.02 for L * galaxies, when fixing the baryon fraction Ω b /Ω m = 0.17 and the Hubble parameter h = 0.72; cosmological interpretation is given in a companion paper.

We measure the large-scale real-space power spectrum P (k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.01 h/Mpc < k < 0.2 h/Mpc. Results from the LRG and main galaxy samples are consistent, with the former providing higher signal-to-noise. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. They provide a striking confirmation of the predicted large-scale ΛCDM power spectrum. Combining only SDSS LRG and WMAP data places robust constraints on many cosmological parameters that complement prior analyses of multiple data sets. The LRGs provide independent cross-checks on Ωm and the baryon fraction in good agreement with WMAP. Within the context of flat ΛCDM models, our LRG measurements complement WMAP by sharpening the constraints on the matter density, the neutrino density and the tensor amplitude by about a factor of two, giving Ωm = 0.24±0.02 (1σ), mν ∼ < 0.9 eV (95%) and r < 0.3 (95%). Baryon oscillations are clearly detected and provide a robust measurement of the comoving distance to the median survey redshift z = 0.35 independent of curvature and dark energy properties. Within the ΛCDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Ωtot = 1.05±0.05 from WMAP alone to Ωtot = 1.003 ± 0.010. Assuming Ωtot = 1, the equation of state parameter is constrained to w = −0.94 ± 0.09, indicating the potential for more ambitious future LRG measurements to provide precision tests of the nature of dark energy. All these constraints are essentially independent of scales k > 0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial. k [h/Mpc] Power Pg 0.012 +0.005 −0.004 124884 ± 18775 0.015 +0.003 −0.002 118814 ± 29400 0.018 +0.004 −0.002 134291 ± 21638 0.021 +0.004 −0.003 58644 ± 16647 0.024 +0.004 −0.003 105253 ± 12736 0.028 +0.005 −0.003 77699 ± 9666 0.032 +0.005 −0.003 57870 ± 7264 0.037 +0.006 −0.004 56516 ± 5466 0.043 +0.008 −0.006 50125 ± 3991 0.049 +0.008 −0.007 45076 ± 2956 0.057 +0.009 −0.007 39339 ± 2214 0.065 +0.010 −0.008 39609 ± 1679 0.075 +0.011 −0.009 31566 ± 1284 0.087 +0.