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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 luminosity and color dependence of galaxy clustering in the largest-ever galaxy redshift survey, the main galaxy sample of the Sloan Digital Sky Survey (SDSS) Seventh Data Release (DR7). We focus on the projected correlation function w p (r p ) of volume-limited samples, extracted from the parent sample of ∼ 700, 000 galaxies over 8000 deg 2 , extending up to redshift of 0.25. We interpret our measurements using halo occupation distribution (HOD) modeling assuming a ΛCDM cosmology (inflationary cold dark matter with a cosmological constant). The amplitude of w p (r p ) grows slowly with luminosity for L < L * and increases sharply at higher luminosities, with a large-scale bias factor b(> L) × (σ 8 /0.8) = 1.06 + 0.21(L/L * ) 1.12 , where L is the sample luminosity threshold. At fixed luminosity, redder galaxies exhibit a higher amplitude and steeper correlation function, a steady trend that runs through the "blue cloud" and "green valley" and continues across the "red sequence." The cross-correlation of red and blue galaxies is close to the geometric mean of their autocorrelations, dropping slightly below at r p < 1 h −1 Mpc. The luminosity trends for the red and blue galaxy populations separately are strikingly different. Blue galaxies show a slow but steady increase of clustering strength with luminosity, with nearly constant shape of w p (r p ). The large-scale clustering of red galaxies shows little luminosity dependence until a sharp increase at L > 4L * , but the lowest luminosity red galaxies (0.04 − 0.25L * ) show very strong clustering on small scales (r p < 2 h −1 Mpc). Most of the observed trends can be naturally understood within the ΛCDM+HOD framework. The growth of w p (r p ) for higher luminosity galaxies reflects an overall shift in the mass scale of their host dark matter halos, in particular an increase in the minimum host halo mass M min . The mass at which a halo has, on average, one satellite galaxy brighter than L is M 1 ≈ 17M min (L) over most of the luminosity range, with a smaller ratio above L * . The growth and steepening of w p (r p ) for redder galaxies reflects the increasing fraction of galaxies that are satellite systems in high mass halos instead of central systems in low mass halos, a trend that is especially marked at low luminosities. Our extensive measurements, provided in tabular form, will allow detailed tests of theoretical models of galaxy formation, a firm grounding of semi-empirical models of the galaxy population, and new constraints on cosmological parameters from combining real-space galaxy clustering with mass-sensitive statistics such as redshift-space distortions, cluster mass-to-light ratios, and galaxy-galaxy lensing.

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We analyze the halo occupation distribution (HOD) and two-point correlation function of galaxy-size dark matter halos using high-resolution dissipationless simulations of the concordance flat ÃCDM model. The halo samples include both the host halos and the ''subhalos,'' distinct gravitationally bound halos within the virialized regions of larger host systems. We find that the HOD, the probability distribution for a halo of mass M to host a number of subhalos N, is similar to that found in semianalytic and N-body+gasdynamics studies. Its first moment, hN i M , has a complicated shape consisting of a step, a shoulder, and a power-law high-mass tail. The HOD can be described by Poisson statistics at high halo masses but becomes sub-Poisson for hN i M P 4. We show that the HOD can be understood as a combination of the probability for a halo of mass M to host a central galaxy and the probability to host a given number N s of satellite galaxies. The former can be approximated by a steplike function, while the latter can be well approximated by a Poisson distribution, fully specified by its first moment. The first moment of the satellite HOD can be well described by a simple power law hN s i / M with % 1 for a wide range of number densities, redshifts, and different power spectrum normalizations. This formulation provides a simple but accurate model for the halo occupation distribution found in simulations. At z ¼ 0, the twopoint correlation function (CF) of galactic halos can be well fitted by a power law down to $100 h À1 kpc with an amplitude and slope similar to those of observed galaxies. The dependence of correlation amplitude on the number density of objects is in general agreement with results from the Sloan Digital Sky Survey. At redshifts z k 1, we find significant departures from the power-law shape of the CF at small scales, where the CF steepens because of a more pronounced one-halo component. The departures from the power law may thus be easier to detect in high-redshift galaxy surveys than at the present-day epoch. They can be used to put useful constraints on the environments and formation of galaxies. If the deviations are as strong as indicated by our results, the assumption of the single power law often used in observational analyses of high-redshift clustering is dangerous and is likely to bias the estimates of the correlation length and slope of the correlation function.