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 on our theory of gravity. The statistical precision with which redshift-space distortions can now be measured demands better control of our theoretical systematic errors. While many recent studies focus on understanding dark matter clustering in redshift space, galaxies occupy special places in the universe: dark matter haloes. In our detailed study of halo clustering and velocity statistics in 67.5 h
−3 Gpc3 of N-body simulations, we uncover a complex dependence of redshift-space clustering on halo bias. We identify two distinct corrections which affect the halo redshift-space correlation function on quasi-linear scales (∼30-80 h
−1 Mpc): the non-linear mapping between real-space 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) h
−1 Mpc for the monopole (quadrupole) halo correlation functions. The dominant correction to the Kaiser limit in this model scales like b
3. We use standard 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 h
−1 Mpc for the range of halo masses we studied (with b= 1.4-2.8). We find that recent models of halo redshift-space clustering that neglect the corrections from the bispectrum and higher order terms from the non-linear real-space 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 the real-space clustering of haloes is the same as the one that determines their pairwise infall velocity amplitude at the per cent level.
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. A standard halo occupation distribution model ...evaluated near the best-fitting Planck Λ cold dark matter (ΛCDM) cosmology provides a good fit to the observed anisotropic clustering, and implies a normalization for the peculiar velocity field of M ∼ 2 × 1013
h
−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 ΛCDM 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 Fisher matrix projections for future cosmological parameter measurements, including neutrino masses, Dark Energy, curvature, modified gravity, the inflationary perturbation spectrum, ...non-Gaussianity, and dark radiation. We focus on DESI and generally redshift surveys (BOSS, HETDEX, eBOSS, Euclid, and WFIRST), but also include CMB (Planck) and weak gravitational lensing (DES and LSST) constraints. The goal is to present a consistent set of projections, for concrete experiments, which are otherwise scattered throughout many papers and proposals. We include neutrino mass as a free parameter in most projections, as it will inevitably be relevant - DESI and other experiments can measure the sum of neutrino masses to ~ 0.02 eV or better, while the minimum possible sum is ~ 0.06 eV. We note that constraints on Dark Energy are significantly degraded by the presence of neutrino mass uncertainty, especially when using galaxy clustering only as a probe of the BAO distance scale (because this introduces additional uncertainty in the background evolution after the CMB epoch). Using broadband galaxy power becomes relatively more powerful, and bigger gains are achieved by combining lensing survey constraints with redshift survey constraints. We do not try to be especially innovative, e.g., with complex treatments of potential systematic errors - these projections are intended as a straightforward baseline for comparison to more detailed analyses.
Abstract
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 parameter H from the baryon acoustic oscillation (BAO) method, in combination with 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 Ω
K
= 0.0003 ± 0.0026 and a dark energy equation-of-state parameter w = −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 H
0 = 67.3 ± 1.0 km s−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 H
0 = 67.8 ± 1.2 km s−1 Mpc−1. Assuming flat ΛCDM, we find Ωm = 0.310 ± 0.005 and H
0 = 67.6 ± 0.5 km s−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 distance scale measurements from the baryon acoustic oscillation signal in the constant stellar mass and low-redshift sample samples from the Data Release 12 of the Baryon Oscillation ...Spectroscopic Survey. The total volume probed is 14.5 Gpc3, a 10 per cent increment from Data Release 11. From an analysis of the spherically averaged correlation function, we infer a distance to z = 0.57 of
$D_V(z)r^{\rm fid}_{\rm d}/r_{\rm d} = 2028\pm 21$
Mpc and a distance to z = 0.32 of
$D_V(z)r^{\rm fid}_{\rm d}/r_{\rm d} = 1264\pm 22$
Mpc assuming a cosmology in which
$r^{\rm fid}_{\rm d} = 147.10$
Mpc. From the anisotropic analysis, we find an angular diameter distance to z = 0.57 of
$D_{\rm A}(z)r^{\rm fid}_{\rm d}/r_{\rm d} = 1401\pm 21$
Mpc and a distance to z = 0.32 of 981 ± 20 Mpc, a 1.5 and 2.0 per cent measurement, respectively. The Hubble parameter at z = 0.57 is
$H(z)r_{\rm d}/r^{\rm fid}_{\rm d} = 100.3\pm 3.7$
km s−1 Mpc−1 and its value at z = 0.32 is 79.2 ± 5.6 km s−1 Mpc−1, a 3.7 and 7.1 per cent measurement, respectively. These cosmic distance scale constraints are in excellent agreement with a Λ cold dark matter model with cosmological parameters released by the recent Planck 2015 results.
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 w
p, 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.
We present a fast method for producing mock galaxy catalogues that can be used to compute the covariance of large-scale clustering measurements and test analysis techniques. Our method populates a ...second-order Lagrangian perturbation theory (2LPT) matter field, where we calibrate masses of dark matter haloes by detailed comparisons with N-body simulations. We demonstrate that the clustering of haloes is recovered at ∼10 per cent accuracy. We populate haloes with mock galaxies using a halo occupation distribution (HOD) prescription, which has been calibrated to reproduce the clustering measurements on scales between 30 and 80 h
−1 Mpc. We compare the sample covariance matrix from our mocks with analytic estimates, and discuss differences. We have used this method to make catalogues corresponding to Data Release 9 of the Baryon Oscillation Spectroscopic Survey (BOSS), producing 600 mock catalogues of the 'CMASS' galaxy sample. These mocks have enabled detailed tests of methods and errors, and have formed an integral part of companion analyses of these galaxy data.
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 w
0 = −1.13 ± 0.12 and w
a = 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.
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 and main samples, and also include the 2-degree Field Galaxy Redshift Survey data. In total, this sample comprises 893 319 galaxies over 9100 deg2. Baryon acoustic oscillations (BAO) 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 rs(zd)/DV(0.275) = 0.1390 ± 0.0037 (2.7 per cent accuracy), where rs(zd) is the comoving sound horizon at the baryon-drag epoch, DV(z) ≡(1 +z)2D2Acz/H(z)1/3, DA(z) is the angular diameter distance and H(z) is the Hubble parameter. We find an almost independent constraint on the ratio of distances DV(0.35)/DV(0.2) = 1.736 ± 0.065, which is consistent at the 1.1σ level with the best-fitting Λ cold dark matter model obtained when combining our z= 0.275 distance constraint with the Wilkinson Microwave Anisotropy Probe 5-year (WMAP5) 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 Ωbh2 and Ωc h2, and combining our BAO distance measurements with those from the Union supernova sample, places a tight constraint on Ωm= 0.286 ± 0.018 and H0= 68.2 ± 2.2 km s−1 Mpc−1 that is robust to allowing Ωk≠ 0 and w≠−1. This result is independent of the behaviour of dark energy at redshifts greater than those probed by the BAO and supernova measurements. Combining these data sets with the full WMAP5 likelihood constraints provides tight constraints on both Ωk=−0.006 ± 0.008 and w=−0.97 ± 0.10 for a constant dark energy equation of state.
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 σ8(Ωm/0.25)0.41 = 0.832±0.033 constraint from Rozo et al. (2009) derived from the SDSS maxBCG Cluster Catalog. In a ΛCDM model and when combined with WMAP5 constraints, these low-redshift measurements constrain ∑mν < 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 ∑mν < 0.3eV. 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≠−1 and by studying a model with coupling between dark energy and dark matter, which allows for variation in w, Ωk, and dark coupling strength ξ. When combining CMB, H0 and the SDSS LRG halo power spectrum from Reid et al. 2009, we find that in this very general model, ∑mν < 0.51 eV with 95% confidence. If we allow the number of relativistic species Nrel to vary in a ΛCDM model with ∑mν = 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.
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