A 2.5% measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies

We perform the first fit to the anisotropic clustering of SDSS-III CMASS DR10 galaxies on scales of ~ 0.8 - 32 Mpc/h. A standard halo occupation distribution model evaluated near the best fit Planck LCDM cosmology provides a good fit to the observed anisotropic clustering, and implies a normalization for the peculiar velocity field of M ~ 2 x 10^13 Msun/h halos of f*sigma8(z=0.57) = 0.450 +/- 0.011. Since this constraint includes both quasi-linear and non-linear scales, it should severely constrain modified gravity models that enhance pairwise infall velocities on these scales. Though model dependent, our measurement represents a factor of 2.5 improvement in precision over the analysis of DR11 on large scales, f*sigma8(z=0.57) = 0.447 +/- 0.028, and is the tightest single constraint on the growth rate of cosmic structure to date. Our measurement is consistent with the Planck LCDM prediction of 0.480 +/- 0.010 at the ~1.9 sigma level. Assuming a halo mass function evaluated at the best fit Planck cosmology, we also find that 10% of CMASS galaxies are satellites in halos of mass M ~ 6 x 10^13 Msun/h. While none of our tests and model generalizations indicate systematic errors due to an insufficiently detailed model of the galaxy-halo connection, the precision of these first results warrant further investigation into the modeling uncertainties and degeneracies with cosmological parameters.

The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: measurements of the growth of structure and expansion rate at z=0.57 from anisotropic clustering

We analyze the anisotropic clustering of massive galaxies from the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) sample, which consists of 264,283 galaxies in the redshift range 0.43 < z < 0.7 spanning 3,275 square degrees. Both peculiar velocities and errors in the assumed redshift-distance relation (Alcock-Paczynski effect) generate correlations between clustering amplitude and orientation with respect to the line-of-sight. Together with the sharp baryon acoustic oscillation (BAO) standard ruler, our measurements of the broadband shape of the monopole and quadrupole correlation functions simultaneously constrain the comoving angular diameter distance (2190 +/- 61 Mpc) to z=0.57, the Hubble expansion rate at z=0.57 (92.4 +/- 4.5 km/s/Mpc), and the growth rate of structure at that same redshift (d sigma8/d ln a = 0.43 +/- 0.069). Our analysis provides the best current direct determination of both DA and H in galaxy clustering data using this technique. If we further assume a LCDM expansion history, our growth constraint tightens to d sigma8/d ln a = 0.415 +/- 0.034. In combination with the cosmic microwave background, our measurements of DA, H, and growth all separately require dark energy at z > 0.57, and when combined imply Omega_{Lambda} = 0.74 +/- 0.016, independent of the Universes evolution at z<0.57. In our companion paper (Samushia et al. prep), we explore further cosmological implications of these observations.

Towards an accurate model of the redshift space clustering of halos in the quasilinear regime

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for measuring the build-up of cosmological structure, which depends both on the expansion rate of the Universe and our theory of gravity. Galaxies occupy dark matter halos, whose redshift space clustering has a complex dependence on bias that cannot be inferred from the behavior of matter. We identify two distinct corrections on quasilinear scales (~ 30-80 Mpc/h): the non-linear mapping between real and redshift space positions, and the non-linear suppression of power in the velocity divergence field. We model the first non-perturbatively using the scale-dependent Gaussian streaming model, which we show is accurate at the <0.5 (2) per cent level in transforming real space clustering and velocity statistics into redshift space on scales s>10 (s>25) Mpc/h for the monopole (quadrupole) halo correlation functions. We use perturbation theory to predict the real space pairwise halo velocity statistics. Our fully analytic model is accurate at the 2 per cent level only on scales s > 40 Mpc/h. Recent models that neglect the corrections from the bispectrum and higher order terms from the non-linear real-to-redshift space mapping will not have the accuracy required for current and future observational analyses. Finally, we note that our simulation results confirm the essential but non-trivial assumption that on large scales, the bias inferred from real space clustering of halos is the same one that determines their pairwise infall velocity amplitude at the per cent level.

Non-Gaussian halo assembly bias

The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, f_NL, offers a promising avenue towards constraining primordial non-Gaussianity with large-scale structure surveys. In this paper, we present the first detection of the dependence of the non-Gaussian halo bias on halo formation history using N-body simulations. We also present an analytic derivation of the expected signal based on the extended Press-Schechter formalism. In excellent agreement with our analytic prediction, we find that the halo formation history-dependent contribution to the non-Gaussian halo bias (which we call non-Gaussian halo assembly bias) can be factorized in a form approximately independent of redshift and halo mass. The correction to the non-Gaussian halo bias due to the halo formation history can be as large as 100%, with a suppression of the signal for recently formed halos and enhancement for old halos. This could in principle be a problem for realistic galaxy surveys if observational selection effects were to pick galaxies occupying only recently formed halos. Current semi-analytic galaxy formation models, for example, imply an enhancement in the expected signal of ~23% and ~48% for galaxies at z=1 selected by stellar mass and star formation rate, respectively.

Robust Neutrino Constraints by Combining Low Redshift Observations with the CMB

We illustrate how recently improved low-redshift cosmological measurements can tighten constraints on neutrino properties. In particular we examine the impact of the assumed cosmological model on the constraints. We first consider the new HST H0 = 74.2 +/- 3.6 measurement by Riess et al. (2009) and the sigma8*(Omegam/0.25)^0.41 = 0.832 +/- 0.033 constraint from Rozo et al. (2009) derived from the SDSS maxBCG Cluster Catalog. In a Lambda CDM model and when combined with WMAP5 constraints, these low-redshift measurements constrain sum mnu<0.4 eV at the 95% confidence level. This bound does not relax when allowing for the running of the spectral index or for primordial tensor perturbations. When adding also Supernovae and BAO constraints, we obtain a 95% upper limit of sum mnu<0.3 eV. We test the sensitivity of the neutrino mass constraint to the assumed expansion history by both allowing a dark energy equation of state parameter w to vary, and by studying a model with coupling between dark energy and dark matter, which allows for variation in w, Omegak, and dark coupling strength xi. When combining CMB, H0, and the SDSS LRG halo power spectrum from Reid et al. 2009, we find that in this very general model, sum mnu < 0.51 eV with 95% confidence. If we allow the number of relativistic species Nrel to vary in a Lambda CDM model with sum mnu = 0, we find Nrel = 3.76^{+0.63}_{-0.68} (^{+1.38}_{-1.21}) for the 68% and 95% confidence intervals. We also report prior-independent constraints, which are in excellent agreement with the Bayesian constraints.

Baryon Acoustic Oscillations in the Sloan Digital Sky Survey Data Release 7 Galaxy Sample

The spectroscopic Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) galaxy sample represents the final set of galaxies observed using the original SDSS target selection criteria. We analyse the clustering of galaxies within this sample, including both the Luminous Red Galaxy (LRG) and Main samples, and also include the 2-degree Field Galaxy Redshift Survey (2dFGRS) data. Baryon Acoustic Oscillations are observed in power spectra measured for different slices in redshift; this allows us to constrain the distance--redshift relation at multiple epochs. We achieve a distance measure at redshift z=0.275, of r_s(z_d)/D_V(0.275)=0.1390+/-0.0037 (2.7% accuracy), where r_s(z_d) is the comoving sound horizon at the baryon drag epoch, D_V(z)=[(1+z)^2D_A^2cz/H(z)]^(1/3), D_A(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances D_V(0.35)/D_V(0.2)=1.736+/-0.065, which is consistent at the 1.1sigma level with the best fit Lambda-CDM model obtained when combining our z=0.275 distance constraint with the WMAP 5-year data. The offset is similar to that found in previous analyses of the SDSS DR5 sample, but the discrepancy is now of lower significance, a change caused by a revised error analysis and a change in the methodology adopted, as well as the addition of more data. Using WMAP5 constraints on Omega_bh^2 and Omega_ch^2, and combining our BAO distance measurements with those from the Union Supernova sample, places a tight constraint on Omega_m=0.286+/-0.018 and H_0 = 68.2+/-2.2km/s/Mpc that is robust to allowing curvature and non-Lambda dark energy. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. (abridged)

Cosmological Constraints from the Clustering of the Sloan Digital Sky Survey DR7 Luminous Red Galaxies

We present the power spectrum of the reconstructed halo density field derived from a sample of Luminous Red Galaxies (LRGs) from the Sloan Digital Sky Survey Seventh Data Release (DR7). The halo power spectrum has a direct connection to the underlying dark matter power for k <= 0.2 h/Mpc, well into the quasi-linear regime. This enables us to use a factor of ~8 more modes in the cosmological analysis than an analysis with kmax = 0.1 h/Mpc, as was adopted in the SDSS team analysis of the DR4 LRG sample (Tegmark et al. 2006). The observed halo power spectrum for 0.02 < k < 0.2 h/Mpc is well-fit by our model: chi^2 = 39.6 for 40 degrees of freedom for the best fit LCDM model. We find Omega_m h^2 * (n_s/0.96)^0.13 = 0.141^{+0.009}_{-0.012} for a power law primordial power spectrum with spectral index n_s and Omega_b h^2 = 0.02265 fixed, consistent with CMB measurements. The halo power spectrum also constrains the ratio of the comoving sound horizon at the baryon-drag epoch to an effective distance to z=0.35: r_s/D_V(0.35) = 0.1097^{+0.0039}_{-0.0042}. Combining the halo power spectrum measurement with the WMAP 5 year results, for the flat LCDM model we find Omega_m = 0.289 +/- 0.019 and H_0 = 69.4 +/- 1.6 km/s/Mpc. Allowing for massive neutrinos in LCDM, we find sum m_{ u} < 0.62 eV at the 95% confidence level. If we instead consider the effective number of relativistic species Neff as a free parameter, we find Neff = 4.8^{+1.8}_{-1.7}. Combining also with the Kowalski et al. (2008) supernova sample, we find Omega_{tot} = 1.011 +/- 0.009 and w = -0.99 +/- 0.11 for an open cosmology with constant dark energy equation of state w.

Luminous Red Galaxy Halo Density Field Reconstruction and Application to Large Scale Structure Measurements

The complex relationship between the galaxy density field and the underlying matter field limits our ability to extract cosmological constraints from galaxy redshift surveys. Our approach is to use halos rather than galaxies to trace the underlying mass distribution. We identify Fingers-of-God (FOGs) and replace multiple galaxies in each FOG with a single halo object. This removes the nonlinear contributions of satellite galaxies, the one-halo term. We test our method on a large set of high-fidelity mock SDSS Luminous Red Galaxy (LRG) catalogs. We find that the aggressive FOG compression algorithm adopted in the LRG P(k) analysis of Tegmark et al. (2006) leads to a ~10% correction to the underlying matter power spectrum at k = 0.1 h/Mpc and ~40% correction at k=0.2 h/Mpc, thereby compromising the cosmological constraints. In contrast, the power spectrum of our reconstructed halo density field deviates from the underlying matter power spectrum by less than 1% for k less than 0.1 h/Mpc and less than 4% for k less than 0.2 h/Mpc. The reconstructed halo density field also removes the bias in the measurement of the redshift space distortion parameter beta induced by the FOG smearing of the linear redshift space distortions.

Constraining the LRG Halo Occupation Distribution using Counts-in-Cylinders

The low number density of the Sloan Digital Sky Survey (SDSS) Luminous Red Galaxies (LRGs) suggests that LRGs occupying the same dark matter halo can be separated from pairs occupying distinct dark matter halos with high fidelity. We present a new technique, Counts-in-Cylinders (CiC), to constrain the parameters of the satellite contribution to the LRG Halo-Occupation Distribution (HOD). For a fiber collision-corrected SDSS spectroscopic LRG subsample at 0.16 < z < 0.36, we find the CiC multiplicity function is fit by a halo model where the average number of satellites in a halo of mass M is <Nsat(M)> = ((M - Mcut)/M1)^alpha with Mcut = 5.0 +1.5/-1.3 (+2.9/-2.6) X 10^13 Msun, M1 = 4.95 +0.37/-0.26 (+0.79/-0.53) X 10^14 Msun, and alpha = 1.035 +0.10/-0.17 (+0.24/-0.31) at the 68% and 95% confidence levels using a WMAP3 cosmology and z=0.2 halo catalog. Our method tightly constrains the fraction of LRGs that are satellite galaxies, 6.36 +0.38/-0.39, and the combination Mcut/10^{14} Msun + alpha = 1.53 +0.08/-0.09 at the 95% confidence level. We also find that mocks based on a halo catalog produced by a spherical overdensity (SO) finder reproduce both the measured CiC multiplicity function and the projected correlation function, while mocks based on a Friends-of-Friends (FoF) halo catalog has a deficit of close pairs at ~1 Mpc/h separations. Because the CiC method relies on higher order statistics of close pairs, it is robust to the choice of halo finder. In a companion paper we will apply this technique to optimize Finger-of-God (FOG) compression to eliminate the 1-halo contribution to the LRG power spectrum.