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.

In this paper we present a clustering analysis of quasi‐stellar objects (QSOs) using over 20 000 objects from the final catalogue of the 2dF QSO Redshift Survey (2QZ), measuring the redshift‐space two‐point correlation function, ξ(s). When averaged over the redshift range 0.3 < z < 2.2 we find that ξ(s) is flat on small scales, steepening on scales above ∼25 h−1 Mpc. In a WMAP/2dF cosmology (Ωm= 0.27, ΩΛ= 0.73) we find a best‐fitting power law with s0= 5.48+0.42−0.48 h−1 Mpc and γ= 1.20 ± 0.10 on scales s= 1 to 25 h−1 Mpc. We demonstrate that non‐linear redshift‐space distortions have a significant effect on the QSO ξ(s) at scales less than ∼10 h−1 Mpc. A cold dark matter model assuming WMAP/2dF cosmological parameters is a good description of the QSO ξ(s) after accounting for non‐linear clustering and redshift‐space distortions, and allowing for a linear bias at the mean redshift of bQ(z= 1.35) = 2.02 ± 0.07. We subdivide the 2QZ into 10 redshift intervals with effective redshifts from z= 0.53 to 2.48. We find a significant increase in clustering amplitude at high redshift in the WMAP/2dF cosmology. The QSO clustering amplitude increases with redshift such that the integrated correlation function, , within 20 h−1 Mpc is and . We derive the QSO bias and find it to be a strong function of redshift with bQ(z= 0.53) = 1.13 ± 0.18 and bQ(z= 2.48) = 4.24 ± 0.53. We use these bias values to derive the mean dark matter halo (DMH) mass occupied by the QSOs. At all redshifts 2QZ QSOs inhabit approximately the same mass DMHs with MDH= (3.0 ± 1.6) × 1012 h−1  M⊙, which is close to the characteristic mass in the Press–Schechter mass function, M*, at z= 0. These results imply that L*Q QSOs at z∼ 0 should be largely unbiased. If the relation between black hole (BH) mass and MDH or host velocity dispersion does not evolve, then we find that the accretion efficiency (L/LEdd) for L*Q QSOs is approximately constant with redshift. Thus the fading of the QSO population from z∼ 2 to ∼0 appears to be due to less massive BHs being active at low redshift. We apply different methods to estimate, tQ, the active lifetime of QSOs and constrain tQ to be in the range 4 × 106–6 × 108 yr at z∼ 2. We test for any luminosity dependence of QSO clustering by measuring ξ(s) as a function of apparent magnitude (equivalent to luminosity relative to L*Q). However, we find no significant evidence of luminosity‐dependent clustering from this data set.

We study the distribution of cosmic voids and void galaxies using Sloan Digital Sky Survey Data Release 7 (SDSS DR7). Using the VoidFinder algorithm based on the original VoidFinder method devised by El‐Ad & Piran and implemented by Hoyle & Vogeley, we identify 1054 statistically significant voids in the Northern galactic hemisphere with radii > 10 h−1 Mpc. The filling factor of voids in the sample volume is 62 per cent. The largest void is just over 30 h−1 Mpc in effective radius. The median effective radius is 17 h−1 Mpc. The voids are found to be significantly underdense, with density contrast δ < − 0.85 at the edges of the voids. The radial‐density profiles of these voids are similar to predictions of dynamically distinct underdensities in gravitational theory. We find 8046 galaxies brighter than Mr=− 20.09 within the voids, accounting for 7 per cent of the galaxies. We compare the results of VoidFinder on SDSS DR7 to mock catalogues generated from a smoothed particle hydrodynamics (SPH) halo model simulation as well as other Λ cold dark matter (ΛCDM) simulations and find similar void fractions and void sizes in the data and simulations. This catalogue is made publicly available at http://www.physics.drexel.edu/~pan/VoidCatalog for download.