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We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample (DR14Q).We measure the redshift space distortions using the power-spectrum monopole, quadrupole, and hexadecapole inferred from 148 659 quasars between redshifts 0.8 and 2.2, covering a total sky footprint of 2112.9 deg2. We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, fσ8, and the Alcock-Paczynski dilation scales that allow constraints to be placed on the angular diameter distance DA(z) and the Hubble H(z) parameter. At the effective redshift of zeff = 1.52, fσ8(zeff) = 0.420 ± 0.076, H(zeff) = [162 ± 12] (r sfid/rs) kms-1 Mpc-1, and DA(zeff) = [1.85 ± 0.11] × 103 (rs/r sfid) Mpc, where rs is the comoving sound horizon at the baryon drag epoch and the superscript 'fid' stands for its fiducial value. The errors take into account the full error budget, including systematics and statistical contributions. These results are in full agreement with the current Λ-Cold Dark Matter cosmological model inferred from Planck measurements. Finally, we compare our measurements with other eBOSS companion papers and find excellent agreement, demonstrating the consistency and complementarity of the different methods used for analysing the data.

We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147 000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts 0.8 < z < 2.2 and measure their spherically averaged clustering in both configuration and Fourier space. Our observational data set and the 1400 simulated realizations of the data set allow us to detect a preference for BAO that is greater than 2.8σ. We determine the spherically averaged BAO distance to z = 1.52 to 3.8 per cent precision: DV (z = 1.52) = 3843 ± 147 (rd/rd,fid) Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flatΛCDMbest-fitting cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find ΩΛ > 0 at 6.6s significance when testing a ΛCDM model with free curvature.

We present cosmological results from the final galaxy clustering data set of the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy sample comprises 1.2 million massive galaxies over an effective area of 9329 deg2 and volume of 18.7 Gpc3, divided into three partially overlapping redshift slices centred at effective redshifts 0.38, 0.51 and 0.61. We measure the angular diameter distance DM and Hubble parameterHfrom the baryon acoustic oscillation (BAO) method, in combinationwith a cosmic microwave background prior on the sound horizon scale, after applying reconstruction to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the pre-reconstruction density field, we measure the product DMH from the Alcock-Paczynski (AP) effect and the growth of structure, quantified by fσ8(z), from redshift-space distortions (RSD). We combine individual measurements presented in seven companion papers into a set of consensus values and likelihoods, obtaining constraints that are tighter and more robust than those from any one method; in particular, the AP measurement from sub-BAO scales sharpens constraints from post-reconstruction BAOs by breaking degeneracy between DM and H. Combined with Planck 2016 cosmic microwave background measurements, our distance scale measurements simultaneously imply curvature ωK = 0.0003 ± 0.0026 and a dark energy equation-of-state parameter ω =-1.01 ± 0.06, in strong affirmation of the spatially flat cold dark matter (CDM) model with a cosmological constant (ΛCDM). Our RSD measurements of fσ8, at 6 per cent precision, are similarly consistent with this model. When combined with supernova Ia data, we find H0 = 67.3 ± 1.0 kms-1 Mpc-1 even for our most general dark energy model, in tension with some direct measurements. Adding extra relativistic species as a degree of freedom loosens the constraint only slightly, to H0 = 67.8 ± 1.2 kms-1 Mpc-1. Assuming flat ΛCDM, we find ωm = 0.310 ± 0.005 and H0 = 67.6 ± 0.5 kms-1 Mpc-1, and we find a 95 per cent upper limit of 0.16 eV c-2 on the neutrino mass sum.

We present a measurement of the linear growth rate of structure, f, from the Sloan Digital Sky Survey III (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 (DR12) using convolution Lagrangian perturbation theory (CLPT) with Gaussian streaming redshift space distortions (GSRSD) to model the two-point statistics of BOSS galaxies in DR12. The BOSS-DR12 data set includes 1198 006 massive galaxies spread over the redshift range 0.2 < z < 0.75. These galaxy samples are categorized in three redshift bins. Using CLPT-GSRSD in our analysis of the combined sample of the three redshift bins, we report measurements of fσ8 for the three redshift bins. We find fσ8 = 0.430 ± 0.054 at zeff = 0.38, fσ8 = 0.452 ± 0.057 at zeff = 0.51 and fσ8 = 0.457 ± 0.052 at zeff = 0.61. Our results are consistent with the predictions of Planck Λ cold dark matter-general relativity. Our constraints on the growth rates of structure in the Universe at different redshifts serve as a useful probe, which can help distinguish between a model of the Universe based on dark energy and models based on modified theories of gravity. This paper is part of a set that analyses the final galaxy clustering data set from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al., to produce the final cosmological constraints from BOSS.

We present an anisotropic analysis of the baryon acoustic oscillation (BAO) scale in the twelfth and final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). We independently analyse the LOWZ and CMASS galaxy samples: the LOWZ sample contains 361 762 galaxies with an effective redshift of zLOWZ = 0.32; the CMASS sample consists of 777 202 galaxies with an effective redshift of zCMASS = 0.57. We extract the BAO peak position from the monopole power-spectrum moment, α0, and from the μ2 moment, α2, where μ is the cosine of the angle to the line of sight. The μ2-moment provides equivalent information to that available in the quadrupole but is simpler to analyse. After applying a reconstruction algorithm to reduce the BAO suppression by bulk motions, we measure the BAO peak position in the monopole and μ2-moment, which are related to radial and angular shifts in scale. We report H(zLOWZ)rs(zd) = (11.60 ± 0.60) × 103 km s-1 and DA(zLOWZ)/rs(zd) = 6.66 ± 0.16 with a cross-correlation coefficient of rHDA = 0.41, for the LOWZ sample; and H(zCMASS)rs(zd) = (14.56 ± 0.37) × 103 km s-1 and DA(zCMASS)/rs(zd) = 9.42 ± 0.13 with a cross-correlation coefficient of rHDA = 0.47, for the CMASS sample. We demonstrate that our results are not affected by the fiducial cosmology assumed for the analysis. We combine these results with the measurements of the BAO peak position in the monopole and quadrupole correlation function of the same data set (Cuesta et al. 2016, companion paper) and report the consensus values: H(zLOWZ)rs(zd) = (11.63 ± 0.69) × 103 km s-1 and DA(zLOWZ)/rs(zd) = 6.67 ± 0.15 with rHDA = 0.35 for the LOWZ sample; H(zCMASS)rs(zd) = (14.67 ± 0.42) × 103 km s-1 and DA(zCMASS)/rs(zd) = 9.47 ± 0.12 with rHDA = 0.52 for the CMASS sample.

We measure and analyse the clustering of the Baryon Oscillation SpectroscopicSurvey (BOSS) relative to the line-of-sight (LOS), for LOWZ and CMASS galaxysamples drawn from the final Data Release 12 (DR12). The LOWZ sample contains361\,762 galaxies with an effective redshift of $z_{\rm lowz}=0.32$, and theCMASS sample 777\,202 galaxies with an effective redshift of $z_{\rmcmass}=0.57$. From the power spectrum monopole and quadrupole moments aroundthe LOS, we measure the growth of structure parameter $f$ times the amplitudeof dark matter density fluctuations $\sigma_8$ by modeling the Redshift-SpaceDistortion signal. When the geometrical Alcock-Paczynski effect is alsoconstrained from the same data, we find joint constraints on $f\sigma_8$, theproduct of the Hubble constant and the comoving sound horizon at the baryondrag epoch $H(z)r_s(z_d)$, and the angular distance parameter divided by thesound horizon $D_A(z)/r_s(z_d)$. We find $f(z_{\rm lowz})\sigma_8(z_{\rmlowz})=0.394\pm0.062$, $D_A(z_{\rm lowz})/r_s(z_d)=6.35\pm0.19$, $H(z_{\rmlowz})r_s(z_d)=(11.41\pm 0.56)\,{10^3\rm km}s^{-1}$ for the LOWZ sample, and$f(z_{\rm cmass})\sigma_8(z_{\rm cmass})=0.444\pm0.038$, $D_A(z_{\rmcmass})/r_s(z_d)=9.42\pm0.15$, $H(z_{\rm cmass})r_s(z_d)=(13.92 \pm 0.44)\,{10^3\rm km}s^{-1}$ for the CMASS sample. We find general agreement withprevious BOSS DR11 measurements. Assuming the Hubble parameter and angulardistance parameter are fixed at fiducial $\Lambda$CDM values, we find $f(z_{\rmlowz})\sigma_8(z_{\rm lowz})=0.485\pm0.044$ and $f(z_{\rmcmass})\sigma_8(z_{\rm cmass})=0.436\pm0.022$ for the LOWZ and CMASS samples,respectively.

We use subhalo abundance matching (SHAM) to model the stellar mass function (SMF) and clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) 'CMASS' sample at z ~ 0.5. We introduce a novel method which accounts for the stellar mass incompleteness of CMASS as a function of redshift, and produce CMASS mock catalogues which include selection effects, reproduce the overall SMF, the projected two-point correlation function wp, the CMASS dn/dz, and are made publicly available. We study the effects of assembly bias above collapse mass in the context of 'age matching' and show that these effects are markedly different compared to the ones explored by Hearin et al. at lower stellar masses. We construct two models, one in which galaxy colour is stochastic ('AbM' model) as well as a model which contains assembly bias effects ('AgM' model). By confronting the redshift dependent clustering of CMASS with the predictions from our model, we argue that that galaxy colours are not a stochastic process in high-mass haloes. Our results suggest that the colours of galaxies in high-mass haloes are determined by other halo properties besides halo peak velocity and that assembly bias effects play an important role in determining the clustering properties of this sample.

Observations of redshift-space distortions in spectroscopic galaxy surveys offer an attractive method for observing the build-up of cosmological structure, which depends both on the expansion rate of the Universe and our theory of gravity. In preparation for analysis of redshiftspace distortions from the Baryon Oscillation Spectroscopic Survey (BOSS) final data release, we compare a number of analytic and phenomenological models, specified in configuration space, to mock catalogues derived in different ways from several N-body simulations. The galaxies in each mock catalogue have properties similar to those of the higher redshift galaxies measured by BOSS but differ in the details of how small-scale velocities and halo occupancy are determined. We find that all of the analytic models fit the simulations over a limited range of scales while failing at small scales.We discuss which models are most robust and on which scales they return reliable estimates of the rate of growth of structure: we find that models based on some form of resummation can fit our N-body data for BOSS-like galaxies above 30 h-1 Mpc well enough to return unbiased parameter estimates.

We present the measurements and modelling of the projected and redshift-space clustering of CMASS galaxies in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Data Release 11. For a volume-limited luminous red galaxy sample in the redshift range of 0.48 < z < 0.55, we perform halo occupation distribution modelling of the small- and intermediate-scale (0.1-60 h-1 Mpc) projected and redshift-space two-point correlation functions, with an accurate model built on high-resolution N-body simulations. To interpret the measured redshift-space distortions, the distribution of galaxy velocities must differ from that of the dark matter inside haloes of ~1013-1014 h-1 M⊙, i.e. the data require the existence of galaxy velocity bias. Most notably, central galaxies on average are not at rest with respect to the core of their host haloes, but rather move around it with a 1D velocity dispersion of 0.22-0.04+0.03 times that of the dark matter, implying a spatial offset from the centre at the level of ≲1 per cent of the halo virial radius. The luminous satellite galaxies move more slowly than the dark matter, with velocities 0.86-0.03+0.08 times those of the dark matter, which suggests that the velocity and spatial distributions of these satellites cannot both be unbiased. The constraints mainly arise from the Fingers-of-God effect at non-linear scales and the smoothing to the Kaiser effect in the translinear regime; the robustness of the results is demonstrated by a variety of tests. We discuss the implications of the existence of galaxy velocity bias for investigations of galaxy formation and cosmology.

We perform the first fit to the anisotropic clustering of Sloan Digital Sky Survey III CMASS data release 10 galaxies on scales of ~0.8-32 h-1 Mpc.Astandard halo occupation distribution model evaluated near the best-fitting Planck ? cold dark matter (?CDM) cosmology provides a good fit to the observed anisotropic clustering, and implies a normalization for the peculiar velocity field of M~2 × 1013h-1 M haloes of fσ8(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, fσ8(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 ?CDM prediction of 0.480 ± 0.010 at the ~1.9σ level. Assuming a halo mass function evaluated at the best-fitting Planck cosmology,we also find that 10 per cent of CMASS galaxies are satellites in haloes of mass M ~ 6 × 1013 h-1 M. 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 modelling uncertainties and degeneracies with cosmological parameters.

We present the distance measurement to z = 0.32 using the eleventh data release (DR) of the Sloan Digital Sky Survey-III Baryon Acoustic Oscillation Survey (BOSS). We use 313 780 galaxies of the low-redshift (LOWZ) sample over 7341 square degrees to compute Dv = (1264±25)(rd/rd,fid) - a sub 2 per cent measurement - using the baryon acoustic feature measured in the galaxy two-point correlation function and power spectrum. We compare our results to those obtained in DR10. We study observational systematics in the LOWZ sample and quantify potential effects due to photometric offsets between the northern and southern Galactic caps. We find the sample to be robust to all systematic effects found to impact on the targeting of higher redshift BOSS galaxies and that the observed north-south tensions can be explained by either limitations in photometric calibration or by sample variance, and have no impact on our final result. Our measurement, combined with the baryonic acoustic scale at z = 0.57, is used in Anderson et al. to constrain cosmological parameters. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

We explore the cosmological implications of the angle-averaged correlation function, ξ(s), and the clustering wedges, ξ⊥(s) and ξ∥(s), of the LOWZ and CMASS galaxy samples from Data Releases 10 and 11 of the Sloan Digital Sky Survey III (SDSS-III) Baryon Oscillation Spectroscopic Survey. Our results show no significant evidence for a deviation from the standard Λ cold dark matter model. The combination of the information from our clustering measurements with recent data from the cosmic microwave background is sufficient to constrain the curvature of the Universe to Ωk = 0.0010 ± 0.0029, the total neutrino mass to ∑mν < 0.23 eV (95 per cent confidence level), the effective number of relativistic species to Neff = 3.31 ± 0.27 and the dark energy equation of state to wDE = -1.051 ± 0.076. These limits are further improved by adding information from Type Ia supernovae and baryon acoustic oscillations from other samples. In particular, this data set combination is completely consistent with a time-independent dark energy equation of state, in which case we find wDE = -1.024 ± 0.052. We explore the constraints on the growth rate of cosmic structures assuming f(z) = Ωm(z)γ and obtain γ = 0.69 ± 0.15, consistent with the predictions of general relativity of γ = 0.55. © 2014 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

We use the observed anisotropic clustering of galaxies in the Baryon Oscillation Spectroscopic Survey Data Release 11 CMASS sample to measure the linear growth rate of structure, the Hubble expansion rate and the comoving distance scale. Our sample covers 8498 deg2 and encloses an effective volume of 6 Gpc3 at an effective redshift of z̄ = 0.57. We find fσ8 = 0.441 ± 0.044, H = 93.1 ± 3.0 kms-1 Mpc-1 and DA = 1380 ± 23 Mpc when fitting the growth and expansion rate simultaneously. When we fix the background expansion to the one predicted by spatially flat δ cold dark matter (δCDM) model in agreement with recent Planck results,we find fσ8 =0.447±0.028 (6 per cent accuracy).While our measurements are generally consistent with the predictions of δCDM and general relativity, they mildly favour models in which the strength of gravitational interactions is weaker than what is predicted by general relativity. Combining our measurements with recent cosmic microwave background data results in tight constraints on basic cosmological parameters and deviations from the standard cosmological model. Separately varying these parameters, we find ω = -0.983 ± 0.075 (8 per cent accuracy) and γ = 0.69 ± 0.11 (16 per cent accuracy) for the effective equation of state of dark energy and the growth rate index, respectively. Both constraints are in good agreement with the standard model values of ω = -1 and γ = 0.554. © 2014 The Authors.

Sophisticated analysis of modern large-scale structure surveys requires mock catalogues. Mock catalogues are used to optimize survey design, test reduction and analysis pipelines, make theoretical predictions for basic observables and propagate errors through complex analysis chains.We present a new method, which we call 'quick particle mesh', for generating many large volume, approximate mock catalogues at low computational cost. The method is based on using rapid, low-resolution particle mesh simulations that accurately reproduce the large-scale dark matter density field. Particles are sampled from the density field based on their local density such that they have N-point statistics nearly equivalent to the haloes resolved in high-resolution simulations, creating a set of mock haloes that can be populated using halo occupation methods to create galaxy mocks for a variety of possible target classes. © 2013 The Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society.

We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations (BAO) in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey, which is part of the Sloan Digital Sky Survey III. Our results come from the Data Release 11 (DR11) sample, containing nearly one million galaxies and covering approximately 8500 square degrees and the redshift range 0.2 < z < 0.7. We also compare these results with those from the publicly released DR9 and DR10 samples. Assuming a concordance Λ cold dark matter (ΛCDM) cosmological model, the DR11 sample covers a volume of 13 Gpc3 and is the largest region of the Universe ever surveyed at this density. We measure the correlation function and power spectrum, including density-field reconstruction of the BAO feature. The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, rd, which has a value of rd,fid = 149.28 Mpc in our fiducial cosmology. We find DV = (1264 ± 25 Mpc)(rd/rd,fid) at z = 0.32 and DV = (2056 ± 20 Mpc)(rd/rd,fid) at z = 0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line of sight yields measurements at z = 0.57 of DA = (1421 ± 20 Mpc)(rd/rd,fid) and H = (96.8 ± 3.4 kms-1 Mpc-1)(rd,fid/rd). Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat CDM model with a cosmological constant. © 2014 The Author Published by Oxford University Press on behalf of the Royal Astronomical Society.

We present the measurements of the small-scale clustering for the emission-line galaxy (ELG) sample from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) in the Sloan Digital Sky Survey IV (SDSS-IV). We use conditional abundance matching method to interpret the clustering measurements from 0.34 to |$70\, h^{-1}\, \textrm {Mpc}$|⁠. In order to account for the correlation between properties of ELGs and their environment, we add a secondary connection between star formation rate of ELGs and halo accretion rate. Three parameters are introduced to model the ELG [O  ii ] luminosity and to mimic the target selection of eBOSS ELGs. The parameters in our models are optimized using Markov Chain Monte Carlo (MCMC) method. We find that by conditionally matching star formation rate of galaxies and the halo accretion rate, we are able to reproduce the eBOSS ELG small-scale clustering within 1σ error level. Our best-fitting model shows that the eBOSS ELG sample only consists of |$\sim 12{{\ \rm per\ cent}}$| of all star-forming galaxies, and the satellite fraction of eBOSS ELG sample is 19.3 per cent. We show that the effect of assembly bias is |$\sim 20{{\ \rm per\ cent}}$| on the two-point correlation function and |$\sim 5{{\ \rm per\ cent}}$| on the void probability function at scale of |$r\sim 20 \, h^{-1}\, \rm Mpc$|⁠. [ABSTRACT FROM AUTHOR]

We present 2000 mock galaxy catalogues for the analysis of baryon acoustic oscillations (BAOs) in the Emission Line Galaxy (ELG) sample of the extended Baryon Oscillation Spectroscopic Survey Data Release 16 (eBOSS DR16). Each mock catalogue has a number density of |$6.7 \times 10^{-4} h^3 \rm Mpc^{-3}$|⁠ , covering a redshift range from 0.6 to 1.1. The mocks are calibrated to small-scale eBOSS ELG clustering measurements at scales of |$\lesssim 30\, h^{-1}$| Mpc. The mock catalogues are generated using a combination of GaLAxy Mocks (GLAM) simulations and the quick particle-mesh (QPM) method. GLAM simulations are used to generate the density field, which is then assigned dark matter haloes using the QPM method. Haloes are populated with galaxies using a halo occupation distribution. The resulting mocks match the survey geometry and selection function of the data, and have slightly higher number density that allows room for systematic analysis. The large-scale clustering of mocks at the BAO scale is consistent with data and we present the correlation matrix of the mocks. [ABSTRACT FROM AUTHOR]

We develop a new method, which is based on the optimal redshift weighting scheme, to extract the maximal tomographic information of baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 quasar (DR14Q) survey. We validate our method using the Extended Zel'dovich mocks, and apply our pipeline to the eBOSS DR14Q sample in the redshift range of 0.8 < |$z$| < 2.2. We report a joint measurement of f σ8 and two-dimensional BAO parameters D A and H at four effective redshifts of |$z$| eff = 0.98, 1.23, 1.52, and 1.94, and provide the full data covariance matrix. Using our measurement combined with BOSS DR12, Main Galaxy Sample (MGS), and 6 degree Field Galaxy Survey (6dFGS) BAO measurements, we find that the existence of dark energy is supported by observations at a 7.4σ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be γ = 0.580 ± 0.082, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample. [ABSTRACT FROM AUTHOR]

Fibre-fed multi-object spectroscopic surveys, with their ability to collect an unprecedented number of redshifts, currently dominate large-scale structure studies. However, physical constraints limit these surveys from successfully collecting redshifts from galaxies too close to each other on the focal plane. This ultimately leads to significant systematic effects on galaxy clustering measurements. Using simulated mock catalogues, we demonstrate that fibre collisions have a significant impact on the power spectrum, P(k), monopole and quadrupole that exceeds sample variance at scales smaller than k ∼ 0.1 h Mpc-1. We present two methods to account for fibre collisions in the power spectrum. The first, statistically reconstructs the clustering of fibre-collided galaxy pairs by modelling the distribution of the line-of-sight displacements between them. It also properly accounts for fibre collisions in the shot-noise correction term of the P(k) estimator. Using this method, we recover the true P(k) monopole of the mock catalogues with residuals of <0.5 per cent at k = 0.3 h Mpc-1 and <4 per cent at k = 0.83 h Mpc-1-a significant improvement over existing correction methods. The quadrupole, however, does not improve significantly. The second method models the effect of fibre collisions on the power spectrum as a convolution with a configuration space top-hat function that depends on the physical scale of fibre collisions. It directly computes theoretical predictions of the fibre-collided P(k) multipoles and reduces the influence of smaller scales to a set of nuisance parameters. Using this method, we reliably model the effect of fibre collisions on the monopole and quadrupole down to the scale limits of theoretical predictions. The methods we present in this paper will allow us to robustly analyse galaxy power spectrum multipole measurements to much smaller scales than previously possible. [ABSTRACT FROM AUTHOR]

We extract cosmological information from the anisotropic power-spectrummeasurements from the recently completed Baryon Oscillation Spectroscopic Survey (BOSS), extending the concept of clustering wedges to Fourier space. Making use of new fast-Fourier-transform-based estimators, we measure the power-spectrum clustering wedges of the BOSS sample by filtering out the information of Legendre multipoles ℓ > 4. Our modelling of these measurements is based on novel approaches to describe non-linear evolution, bias and redshift-space distortions, which we test using synthetic catalogues based on large-volume N-body simulations. We are able to include smaller scales than in previous analyses, resulting in tighter cosmological constraints. Using three overlapping redshift bins, we measure the angular-diameter distance, the Hubble parameter and the cosmic growth rate and explore the cosmological implications of our full-shape clustering measurements in combination with cosmic microwave background and Type Ia supernova data. Assuming a Λ cold dark matter (ΛCDM) cosmology, we constrain the matter density #8230; and the Hubble parameter to #8230; , at a confidence level of 68 per cent. We also allow for nonstandard dark energy models and modifications of the growth rate, finding good agreement with the ΛCDM paradigm. For example, we constrain the equation-of-state parameter to #8230;. This paper is part of a set that analyses the final galaxy-clustering data set from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. to produce the final cosmological constraints from BOSS. [ABSTRACT FROM AUTHOR]

We use subhalo abundance matching (SHAM) to model the stellar mass function (SMF) and clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) 'CMASS' sample at z ~ 0.5. We introduce a novel method which accounts for the stellar mass incompleteness of CMASS as a function of redshift, and produce CMASS mock catalogues which include selection effects, reproduce the overall SMF, the projected two-point correlation function wp, the CMASS dn/dz, and are made publicly available. We study the effects of assembly bias above collapse mass in the context of 'age matching' and show that these effects are markedly different compared to the ones explored by Hearin et al. at lower stellar masses. We construct two models, one in which galaxy colour is stochastic ('AbM' model) as well as a model which contains assembly bias effects ('AgM' model). By confronting the redshift dependent clustering of CMASS with the predictions from our model, we argue that that galaxy colours are not a stochastic process in high-mass haloes. Our results suggest that the colours of galaxies in high-mass haloes are determined by other halo properties besides halo peak velocity and that assembly bias effects play an important role in determining the clustering properties of this sample. [ABSTRACT FROM AUTHOR]

Extraction of the Baryon Acoustic Oscillations (BAO) to per cent level accuracy is challenging and demands an understanding of many potential systematics to an accuracy well below 1 per cent, in order to ensure that they do not combine significantly when compared to statistical error of the BAO measurement. Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 11 (DR11) reaches a distance measurement with ∼1 per cent statistical error and this prompts an extensive search for all possible sub-per cent level systematic errors which could previously be safely ignored. In this paper, we analyse the potential systematics in BAO fitting methodology using mocks and data from BOSS DR10 and DR11. We demonstrate the robustness of the fiducial multipole fitting methodology to be at 0.1–0.2 per cent level with a wide range of tests in mock galaxy catalogues pre- and post-reconstruction. We also find the DR10 and DR11 data from BOSS to be robust against changes in methodology at a similar level. This systematic error budget is incorporated into the BOSS DR10 and DR11 BAO measurements. Of the wide range of changes we have investigated, we find that when fitting post-reconstructed data or mocks, the only change which has an effect >0.1 per cent on the best-fitting values of distance measurements is varying the order of the polynomials to describe the broad-band terms (∼0.2 per cent). Finally, we compare an alternative methodology denoted as Clustering Wedges with Multipoles, and find that it is consistent with the standard approach. [ABSTRACT FROM PUBLISHER]

We investigate the cosmological implications of the latest growth of structure measurement from the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 with particular focus on the sum of the neutrino masses, ∑mν. We examine the robustness of the cosmological constraints from the baryon acoustic oscillation (BAO) scale, the Alcock–Paczynski effect and redshift-space distortions (DV/rs, FAP, fσ8) of Beutler et al., when introducing a neutrino mass in the power spectrum template. We then discuss how the neutrino mass relaxes discrepancies between the cosmic microwave background (CMB) and other low-redshift measurements within Λ cold dark matter. Combining our cosmological constraints with 9-year Wilkinson Microwave Anisotropy Probe (WMAP9) yields ∑mν = 0.36 ± 0.14 eV (68 per cent c.l.), which represents a 2.6σ preference for non-zero neutrino mass. The significance can be increased to 3.3σ when including weak lensing results and other BAO constraints, yielding ∑mν = 0.35 ± 0.10 eV (68 per cent c.l.). However, combining CMASS with Planck data reduces the preference for neutrino mass to ∼2σ. When removing the CMB lensing effect in the Planck temperature power spectrum (by marginalizing over AL), we see shifts of ∼1σ in σ8 and Ωm, which have a significant effect on the neutrino mass constraints. In the case of CMASS plus Planck without the AL lensing signal, we find a preference for a neutrino mass of ∑mν = 0.34 ± 0.14 eV (68 per cent c.l.), in excellent agreement with the WMAP9+CMASS value. The constraint can be tightened to 3.4σ yielding ∑mν = 0.36 ± 0.10 eV (68 per cent c.l.) when weak lensing data and other BAO constraints are included. [ABSTRACT FROM AUTHOR]

We analyse the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) CMASS Data Release 11 (DR11) sample, which consists of 690 827 galaxies in the redshift range 0.43 < z < 0.7 and has a sky coverage of 8498 deg2. We perform our analysis in Fourier space using a power spectrum estimator suggested by Yamamoto et al. We measure the multipole power spectra in a self-consistent manner for the first time in the sense that we provide a proper way to treat the survey window function and the integral constraint, without the commonly used assumption of an isotropic power spectrum and without the need to split the survey into subregions. The main cosmological signals exploited in our analysis are the baryon acoustic oscillations and the signal of redshift space distortions, both of which are distorted by the Alcock–Paczynski effect. Together, these signals allow us to constrain the distance ratio DV(zeff)/rs(zd) = 13.89 ± 0.18, the Alcock–Paczynski parameter FAP(zeff) = 0.679 ± 0.031 and the growth rate of structure f (zeff)σ8(zeff) = 0.419 ± 0.044 at the effective redshift zeff = 0.57. We emphasize that our constraints are robust against possible systematic uncertainties. In order to ensure this, we perform a detailed systematics study against CMASS mock galaxy catalogues and N-body simulations. We find that such systematics will lead to 3.1 per cent uncertainty for fσ8 if we limit our fitting range to k = 0.01–0.20 h Mpc−1, where the statistical uncertainty is expected to be three times larger. We did not find significant systematic uncertainties for DV/rs or FAP. Combining our data set with Planck to test General Relativity (GR) through the simple γ-parametrization, where the growth rate is given by $f(z) = \Omega ^{\gamma }_{\rm m}(z)$, reveals a ∼2σ tension between the data and the prediction by GR. The tension between our result and GR can be traced back to a tension in the clustering amplitude σ8 between CMASS and Planck. [ABSTRACT FROM PUBLISHER]

We investigate the luminosity and colour dependence of clustering of CMASS galaxies in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Data Release 10, focusing on projected correlation functions of well-defined samples extracted from the full catalogue of ∼540 000 galaxies at z ∼ 0.5 covering about 6500 deg2. The halo occupation distribution framework is adopted to model the measurements on small and intermediate scales (from 0.02 to 60 h−1 Mpc), infer the connection of galaxies to dark matter haloes and interpret the observed trends. We find that luminous red galaxies in CMASS reside in massive haloes of mass M ∼ 1013–1014 h−1 M⊙ and more luminous galaxies are more clustered and hosted by more massive haloes. The strong small-scale clustering requires a fraction of these galaxies to be satellites in massive haloes, with the fraction at the level of 5–8 per cent and decreasing with luminosity. The characteristic mass of a halo hosting on average one satellite galaxy above a luminosity threshold is about a factor of 8.7 larger than that of a halo hosting a central galaxy above the same threshold. At a fixed luminosity, progressively redder galaxies are more strongly clustered on small scales, which can be explained by having a larger fraction of these galaxies in the form of satellites in massive haloes. Our clustering measurements on scales below 0.4 h−1 Mpc allow us to study the small-scale spatial distribution of satellites inside haloes. While the clustering of luminosity-threshold samples can be well described by a Navarro–Frenk–White profile, that of the reddest galaxies prefers a steeper or more concentrated profile. Finally, we also use galaxy samples of constant number density at different redshifts to study the evolution of luminous red galaxies, and find the clustering to be consistent with passive evolution in the redshift range of 0.5 ≲ z ≲ 0.6. [ABSTRACT FROM AUTHOR]

We provide new constraints on the connection between galaxies in the local universe, identified by the Sloan Digital Sky Survey, and dark matter halos and their constituent substructures in the A-cold dark matter model using WMAP7 cosmological parameters. Predictions for the abundance and clustering properties of dark matter halos, and the relationship between dark matter hosts and substructures, are based on a high-resolution cosmological simulation, the Bolshoi simulation. We associate galaxies with dark matter halos and subhalos using subhalo abundance matching, and perform a comprehensive analysis which investigates the underlying assumptions of this technique including (1) which halo property is most closely associated with galaxy stellar masses and luminosities, (2) how much scatter is in this relationship, and (3) how much subhalos can be stripped before their galaxies are destroyed. The models are jointly constrained by new measurements of the projected two-point galaxy clustering and the observed conditional stellar mass function of galaxies in groups. We find that an abundance matching model that associates galaxies with the peak circular velocity of their halos is in good agreement with the data, when scatter of 0.20 ± 0.03 dex in stellar mass at a given peak velocity is included. This confirms the theoretical expectation that the stellar mass of galaxies is tightly correlated with the potential wells of their dark matter halos before they are impacted by larger structures. The data put tight constraints on the satellite fraction of galaxies as a function of galaxy stellar mass and on the scatter between halo and galaxy properties, and rule out several alternative abundance matching models that have been considered. This will yield important constraints for galaxy formation models, and also provides encouraging indications that the galaxy-halo connection can be modeled with sufficient fidelity for future precision studies of the dark universe. [ABSTRACT FROM AUTHOR]

We use the joint measurement of geometry and growth from anisotropic galaxy clustering in the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 9 (DR9) CMASS sample reported by Reid et al. to constrain dark energy (DE) properties and possible deviations from the general relativity (GR). Assuming GR and taking a prior on the linear matter power spectrum at high redshift from the cosmic microwave background (CMB), anisotropic clustering of the CMASS DR9 galaxies alone constrains Ωm = 0.308 ± 0.022 and 100Ωk = 5.9 ± 4.8 for w = −1, or w = −0.91 ± 0.12 for Ωk = 0. When combined with the full CMB likelihood, the addition of the anisotropic clustering measurements to the spherically averaged baryon acoustic oscillation location increases the constraining power on DE by a factor of 4 in a flat cold dark matter (CDM) cosmology with constant DE equation of state w (giving w = −0.87 ± 0.05). This impressive gain depends on our measurement of both the growth of structure and the Alcock–Paczynski effect, and is not realized when marginalizing over the amplitude of redshift-space distortions. Combining with both the CMB and Type Ia supernovae, we find Ωm = 0.281 ± 0.014 and 1000Ωk = −9.2 ± 5.0 for w = −1, or w0 = −1.13 ± 0.12 and wa = 0.65 ± 0.36 assuming Ωk = 0. Finally, when a ΛCDM background expansion is assumed, the combination of our estimate of the growth rate with previous growth measurements provides tight constraints on the parameters describing possible deviations from GR giving γ = 0.64 ± 0.05. For one-parameter extensions of the flat ΛCDM model, we find a ∼2σ preference either for w > −1 or slower growth than in GR. However, the data are fully consistent with the concordance model, and evidence for these additional parameters is weaker than 2σ. [ABSTRACT FROM AUTHOR]

We place constraints on the average density (ωm) and clustering amplitude (σ8) of matter using a combination of two measurements from the Sloan Digital Sky Survey: the galaxy two-point correlation function, wp (rp), and the mass-to-galaxy-number ratio within galaxy clusters, M/N, analogous to cluster M/L ratios. Our wp (rp) measurements are obtained from DR7 while the sample of clusters is the maxBCG sample, with cluster masses derived from weak gravitational lensing. We construct nonlinear galaxy bias models using the Halo Occupation Distribution (HOD) to fit both wp (rp) and M/N for different cosmological parameters. HOD models that match the same two-point clustering predict different numbers of galaxies in massive halos when ωm or σ8 is varied, thereby breaking the degeneracy between cosmology and bias. We demonstrate that this technique yields constraints that are consistent and competitive with current results from cluster abundance studies, without the use of abundance information. Using wp (rp) and M/N alone, we find Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. &sigma8 = 0.465 ± 0.026, with individual constraints of ωm = 0.29 ± 0.03 and σ8 = 0.85 ± 0.06. Combined with current cosmic microwave background data, these constraints are ωm = 0.290 ± 0.016 and &sigma8 = 0.826 ± 0.020. All errors are 1σ. The systematic uncertainties that the M/N technique are most sensitive to are the amplitude of the bias function of dark matter halos and the possibility of redshift evolution between the SDSS Main sample and the maxBCG cluster sample. Our derived constraints are insensitive to the current level of uncertainties in the halo mass function and in the mass-richness relation of clusters and its scatter, making the M/N technique complementary to cluster abundances as a method for constraining cosmology with future galaxy surveys. [ABSTRACT FROM AUTHOR]

We present an analytic model for the galaxy two-point correlation function in redshift space. The cosmological parameters of the model are the matter density Ωm, power spectrum normalization σ8, and velocity bias of galaxies αv, circumventing the linear theory distortion parameter β and eliminating nuisance parameters for non-linearities. The model is constructed within the framework of the halo occupation distribution (HOD), which quantifies galaxy bias on linear and non-linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of the velocity DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain and αv in models that are constructed to have the same value of β at large scales as well as the same finger-of-god distortions at small scales. [ABSTRACT FROM AUTHOR]

We show how redshift-space distortions of the galaxy correlation function or power spectrum can constrain the matter density parameter Ωm and the linear matter fluctuation amplitude σ8. We improve on previous treatments by adopting a fully non-linear description of galaxy clustering and bias, which allows us to achieve the accuracy demanded by larger galaxy redshift surveys and to break parameter degeneracies by combining large-scale and small-scale distortions. Given an observationally motivated choice of the initial power spectrum shape, we consider different combinations of Ωm and σ8 and find parameters of the galaxy halo occupation distribution (HOD) that yield nearly identical galaxy correlation functions in real space. We use these HOD parameters to populate the dark matter haloes of large N-body simulations, from which we measure redshift-space distortions on small and large scales. We include a velocity bias parameter αv that allows the velocity dispersions of satellite galaxies in haloes to be systematically higher or lower than those of dark matter. Large-scale distortions are determined by the parameter combination , where bg is the bias factor defined by the ratio of galaxy and matter correlation functions, in agreement with the linear theory prediction of parameter degeneracy. However, linear theory does not accurately describe the distortions themselves on scales accessible to our simulations. We provide fitting formulas to estimate β from measurements of the redshift-space correlation function or power spectrum, and we show that these formulas are significantly more accurate than those in the existing literature. On small scales, the ‘FOG’ distortions at projected separations depend on but are independent of σ8, while at intermediate separations they depend on σ8 as well. One can thus use measurements of redshift-space distortions over a wide range of scales to separately determine , and . [ABSTRACT FROM AUTHOR]