Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in Fourier space

We present constraints on local primordial non-Gaussianity (PNG), parametrized through $f^{\rm loc}_{\rm NL}$, using the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample. We measure and analyze the anisotropic clustering of the quasars in Fourier space, testing for the scale-dependent bias introduced by primordial non-Gaussianity on large scales. We derive and employ a power spectrum estimator using optimal weights that account for the redshift evolution of the PNG signal. We find constraints of $-51<f^{\rm loc}_{\rm NL}<21$ at 95% confidence level. These are amont the tightest constraints from Large Scale Structure (LSS) data. Our redshift weighting improves the error bar by 15% in comparison to the unweighted case. If quasars have lower response to PNG, the constraint degrades to $-81<f^{\rm loc}_{\rm NL}<26$, with a 40% improvement over the standard approach. We forecast that the full eBOSS dataset could reach $\sigma_{f^{\rm loc}_{\rm NL}}\simeq 5\text{-}8$ using optimal methods and full range of scales.

Related papers:

title: Planck 2015 results. XVII. Constraints on primordial non-Gaussianity
abstract: The Planck nominal mission cosmic microwave background (CMB) maps yield unprecedented constraints on primordial non-Gaussianity (NG). Using three optimal bispectrum estimators, separable template-fitting (KSW), binned, and modal, we obtain consistent values for the primordial local, equilateral, and orthogonal bispectrum amplitudes, quoting as our final result fNL^local= 2.7+/-5.8, fNL^equil= -42+/-75, and fNL^ortho= -25+\-39 (68% CL statistical). NG is detected in the data; using skew-C_l statistics we find a nonzero bispectrum from residual point sources, and the ISW-lensing bispectrum at a level expected in the LambdaCDM scenario. The results are based on comprehensive cross-validation of these estimators on Gaussian and non-Gaussian simulations, are stable across component separation techniques, pass an extensive suite of tests, and are confirmed by skew-C_l, wavelet bispectrum and Minkowski functional estimators. Beyond estimates of individual shape amplitudes, we present model-independent, 3-dimensional reconstructions of the Planck CMB bispectrum and thus derive constraints on early-Universe scenarios that generate primordial NG, including general single-field models of inflation, excited initial states (non-Bunch-Davies vacua), and directionally-dependent vector models. We provide an initial survey of scale-dependent feature and resonance models. These results bound both general single-field and multi-field model parameter ranges, such as the speed of sound, c_s \geq 0.02 (95% CL), in an effective field theory parametrization, and the curvaton decay fraction r_D \geq 0.15 (95% CL). The Planck data significantly limit the viable parameter space of the ekpyrotic/cyclic scenarios. The amplitude of the 4-point function in the local model tauNL < 2800 (95% CL). These constraints represent the highest precision tests to date of physical mechanisms for the origin of cosmic structure.

title: Probing inflation with CMB polarization
abstract: We summarize the utility of precise cosmic microwave background (CMB) polarization measurements as probes of the physics of inflation. We focus on the prospects for using CMB measurements to differentiate various inflationary mechanisms. In particular, a detection of primordial B‐mode polarization would demonstrate that inflation occurred at a very high energy scale, and that the inflaton traversed a super‐Planckian distance in field space. We explain how such a detection or constraint would illuminate aspects of physics at the Planck scale. Moreover, CMB measurements can constrain the scale‐dependence and non‐Gaussianity of the primordial fluctuations and limit the possibility of a significant isocurvature contribution. Each such limit provides crucial information on the underlying inflationary dynamics. Finally, we quantify these considerations by presenting forecasts for the sensitivities of a future satellite experiment to the inflationary parameters.

title: Constraining primordial non-Gaussianity via a multitracer technique with surveys by Euclid and the Square Kilometre Array
abstract: We forecast future constraints on local-type primordial non-Gaussianity parameter $f_{\rm NL}$ with a photometric galaxy survey by Euclid, a continuum galaxy survey by Square Kilometre Array (SKA), and their combination. We derive a general expression for the covariance matrix of the power spectrum estimates of multiple tracers to show how the so-called multitracer technique improves constraints on $f_{\rm NL}$. In particular we clarify the role of the overlap fraction of multiple tracers and the division method of the tracers. Our Fisher matrix analysis indicates that stringent constraints of $\sigma (f_{\rm NL})\lesssim 1$ can be obtained even with a single survey, assuming five mass bins. When Euclid and SKA phase 1 (2) are combined, constraints on $f_{\rm NL}$ are improved to $\sigma (f_{\rm NL})= 0.61~(0.50)$.

title: Radio galaxy populations and the multitracer technique: pushing the limits on primordial non-Gaussianity
abstract: We explore the use of different radio galaxy populations as tracers of different mass halos and therefore, with different bias properties, to constrain primordial nonGaussianity of the local type. We perform a Fisher matrix analysis based on the predicted auto and cross angular power spectra of these populations, using simulated redshift distributions as a function of detection flux and the evolution of the bias for the different galaxy types (Star forming galaxies, Starburst galaxies, Radio-Quiet Quasars, FRI and FRII AGN galaxies). We show that such a multi-tracer analysis greatly improves the information on non-Gaussianity by drastically reducing the cosmic variance contribution to the overall error budget. By using this method applied to future surveys, we predict a constraint of σfnl = 3.6 on the local non-Gaussian parameter for a galaxy detection flux limit of 10µJy and σfnl = 2.2 for 1 µJy. We show that this significantly improves on the constraints obtained when using the whole undifferentiated populations (σfnl = 48 for 10 µJy and σfnl = 12 for 1 µJy). We conclude that continuum radio surveys alone have the potential to constrain primordial non-Gaussianity to an accuracy at least a factor of two better than the present constraints obtained with Planck data on the CMB bispectrum, opening a window to obtain σfnl � 1 with the Square Kilometer Array.

title: Optimization of spectroscopic surveys for testing non-Gaussianity
abstract: We investigate optimization strategies to measure primordial non-Gaussianity with future spectroscopic surveys. We forecast measurements coming from the 3D galaxy power spectrum and compute constraints on primordial non-Gaussianity parameters f_(NL) and n_(NG). After studying the dependence on those parameters upon survey specifications such as redshift range, area, number density, we assume a reference mock survey and investigate the trade-off between number density and area surveyed. We then define the observational requirements to reach the detection of f_(NL) of order 1. Our results show that while power spectrum constraints on non-Gaussianity from future spectroscopic surveys can be competitive with current CMB limits, measurements from higher-order statistics will be needed to reach a sub unity precision in the measurements of the non-Gaussianity parameter f_(NL).

title: Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis
abstract: The Square Kilometre Array (SKA) will produce spectroscopic surveys of tens to hundreds of millions of neutral hydrogen (HI) galaxies, eventually covering 30,000 deg and reaching out to redshift z & 2. The huge volumes probed by the SKA will allow for some of the best constraints on primordial non-Gaussianity, based on measurements of the large-scale power spectrum. We investigate various observational set-ups for HI galaxy redshift surveys, compatible with the SKA Phase 1 and Phase 2 (full SKA) configurations. We use the corresponding number counts and bias for each survey from realistic simulations and derive the magnification bias and the evolution of source counts directly from these. For the first time, we produce forecasts that fully include the general relativistic effects on the galaxy number counts. These corrections to the standard analysis become important on very large scales, where the signal of primordial non-Gaussianity grows strongest. Our results show that, for the full survey, the non-Gaussianity parameter fNL can be constrained down to σ(fNL) = 1.54. This improves the current limit set by the Planck satellite by a factor of five, using a completely different approach.

title: Constraining ultralarge-scale cosmology with multiple tracers in optical and radio surveys
abstract: Multiple tracers of the cosmic density field, with different bias, number and luminosity evolution, can be used to measure the large-scale properties of the Universe. We show how an optimal combination of tracers can be used to detect general-relativistic effects in the observed density of sources. We forecast for the detectability of these effects, as well as measurements of primordial non-Gaussianity and large-scale lensing magnification with current and upcoming large-scale structure experiments. In particular we quantify the significance of these detections in the short term with experiments such as the Dark Energy Survey (DES), and in the long term with the Large Synoptic Survey Telescope (LSST) and the Square Kilometre Array (SKA). We review the main observational challenges that must be overcome to carry out these measurements.

title: Cosmic infrared background anisotropies as a window into primordial non-Gaussianity
abstract: The angular power spectrum of the cosmic infrared background (CIB) is a sensitive probe of the local primordial bispectrum. CIB measurements are integrated over a large volume so that the scale dependent bias from the primordial non-Gaussianity leaves a strong signal in the CIB power spectrum. Although galactic dust dominates over the non-Gaussian CIB signal, it is possible to mitigate the dust contamination with enough frequency channels, especially if high frequencies such as the Planck 857 GHz channel are available. We show that, in this case, measurements of the cosmic microwave background from future space missions should be able to probe the local bispectrum shape down to an amplitude |f_nl| < 1.

title: Constraining primordial non-Gaussianity with bispectrum and power spectrum from upcoming optical and radio surveys
abstract: We forecast constraints on primordial non-Gaussianity (PNG) and bias parameters from measurements of galaxy power spectrum and bispectrum in future radio continuum and optical surveys. In the galaxy bispectrum, we consider a comprehensive list of effects, including the bias expansion for non-Gaussian initial conditions up to second order, redshift space distortions, redshift uncertainties and theoretical errors. These effects are all combined in a single PNG forecast for the first time. Moreover, we improve the bispectrum modelling over previous forecasts, by accounting for trispectrum contributions. All effects have an impact on final predicted bounds, which varies with the type of survey. We find that the bispectrum can lead to improvements up to a factor $\sim 5$ over bounds based on the power spectrum alone, leading to significantly better constraints for local-type PNG, with respect to current limits from \textit{Planck}. Future radio and photometric surveys could obtain a measurement error of $\sigma(f_{\mathrm{NL}}^{\mathrm{loc}}) \approx 0.2$. In the case of equilateral PNG, galaxy bispectrum can improve upon present bounds only if significant improvements in the redshift determinations of future, large volume, photometric or radio surveys could be achieved. For orthogonal non-Gaussianity, expected constraints are generally comparable to current ones.

title: The Effect of Primordial Non-Gaussianity on Halo Bias
abstract: It has long been known how to analytically relate the clustering properties of the collapsed structures (halos) to those of the underlying dark matter distribution for Gaussian initial conditions. Here we apply the same approach to physically motivated non-Gaussian models. The techniques we use were developed in the 1980s to deal with the clustering of peaks of non-Gaussian density fields. The description of the clustering of halos for non-Gaussian initial conditions has recently received renewed interest, motivated by the forthcoming large galaxy and cluster surveys. For inflationary-motivated non-Gaussianities, we find an analytic expression for the halo bias as a function of scale, mass, and redshift, employing only the approximations of high peaks and large separations.

title: Constraints on local primordial non-Gaussianity from large scale structure
abstract: Recent work has shown that the local non-Gaussianity parameter fNL induces a scale dependent bias, whose amplitude is growing with scale. Here we first rederive this result within the context of the peak–background split formalism and show that it only depends on the assumption of universality of the mass function, assuming that the halo bias only depends on the mass. We then use the extended Press–Schechter formalism to argue that this assumption may be violated and that the scale dependent bias will depend on other properties, such as the merging history of halos. In particular, in the limit of recent mergers we find that the effect is suppressed. Next we use these predictions in conjunction with a compendium of large scale data to put a limit on the value of fNL. When combining all data assuming that the halo occupation depends only on the halo mass, we get a limit of -29 (-65)<fNL<+70 (+93) at 95% (99.7%) confidence. While we use a wide range of data sets, our combined result is dominated by the signal from the SDSS photometric quasar sample. If the latter are modeled as recent mergers then the limits weaken to -31 (-96)<fNL<+70 (+96). These limits are comparable to the strongest current limits from the Wilkinson Anisotropy Probe (WMAP) five-year analysis, with no evidence of a positive signal in fNL. While the method needs to be thoroughly tested against large scale structure simulations with realistic quasar and galaxy formation models, our results indicate that this is a competitive method relative to the cosmic microwave background one and should be further pursued both observationally and theoretically.

title: Primordial non-Gaussianity from the large-scale structure
abstract: Primordial non-Gaussianity is a potentially powerful discriminant of the physical mechanisms that generate the cosmological fluctuations observed today. Any detection of non-Gaussianity would have profound implications for our understanding of cosmic structure formation. In this paper, we review past and current efforts in the search for primordial non-Gaussianity in the large-scale structure of the Universe.

title: Testing Inflation with Large Scale Structure: Connecting Hopes with Reality
abstract: The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude $f_{\rm NL}^{\rm loc}$ ($f_{\rm NL}^{\rm eq}$), natural target levels of sensitivity are $\Delta f_{\rm NL}^{\rm loc, eq.} \simeq 1$. We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.

title: How to evade the sample variance limit on measurements of redshift-space distortions
abstract: We show how to use multiple tracers of large-scale density with different biases to measure the redshift-space distortion parameter β ≡ b−1f ≡ b−1d ln D/d ln a (where D is the growth factor and a the expansion factor), to, as the signal-to-noise (S/N) of a survey increases, much better precision than one could achieve with a single tracer (to arbitrary precision in the low noise limit). In combination with the power spectrum of the tracers this would allow a more precise measurement of the bias-free velocity divergence power spectrum, f2Pm, with the ultimate, zero noise limit, being that f2Pm can be measured as well as would be possible if velocity divergence was observed directly, with maximum rms improvement factor ~ [5.2(β2+2β+2)/β2]1/2 (e.g., 10 times better than a single tracer with β = 0.4). This would allow a determination of fD as a function of redshift with an error as low as ~ 0.1% (again, in the idealized case of the zero noise limit). The ratio b2/b1 can be determined with an even greater precision than β, potentially producing, when measured as a function of scale, an exquisitely sensitive probe of the onset of non-linear bias. We also extend in more detail previous work on the use of the same technique to measure non-Gaussianity. Currently planned redshift surveys are typically designed with S/N ~ 1 on scales of interest, which severely limits the usefulness of our method. Our results suggest that there are potentially large gains to be achieved from technological or theoretical developments that allow higher S/N, or, in the long term, surveys that simply observe a higher number density of galaxies.

title: Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure
abstract: One of the main signatures of primordial non-Gaussianity of the local type is a scale-dependent correction to the bias of large-scale structure tracers such as galaxies or clusters, whose amplitude depends on the bias of the tracers itself. The dominant source of noise in the power spectrum of the tracers is caused by sampling variance on large scales (where the non-Gaussian signal is strongest) and shot noise arising from their discrete nature. Recent work has argued that one can avoid sampling variance by comparing multiple tracers of different bias, and suppress shot noise by optimally weighting halos of different mass. Here we combine these ideas and investigate how well the signatures of non-Gaussian fluctuations in the primordial potential can be extracted from the two-point correlations of halos and dark matter. On the basis of large N-body simulations with local non-Gaussian initial conditions and their halo catalogs we perform a Fisher matrix analysis of the two-point statistics. Compared to the standard analysis, optimal weighting and multiple-tracer techniques applied to halos can yield up to 1 order of magnitude improvements in f{sub NL}-constraints, even if the underlying dark matter density field is not known. In this case one needs to resolve allmore » halos down to 10{sup 10}h{sup -1}M{sub sun} at z=0, while with the dark matter this is already achieved at a mass threshold of 10{sup 12}h{sup -1}M{sub sun}. We compare our numerical results to the halo model and find satisfactory agreement. Forecasting the optimal f{sub NL}-constraints that can be achieved with our methods when applied to existing and future survey data, we find that a survey of 50h{sup -3} Gpc{sup 3} volume resolving all halos down to 10{sup 11}h{sup -1}M{sub sun} at z=1 will be able to obtain {sigma}{sub f{sub N{sub L}}}{approx}1 (68% cl), a factor of {approx}20 improvement over the current limits. Decreasing the minimum mass of resolved halos, increasing the survey volume or obtaining the dark matter maps can further improve these limits, potentially reaching the level of {sigma}{sub f{sub N{sub L}}}{approx}0.1. This precision opens up the possibility to distinguish different types of primordial non-Gaussianity and to probe inflationary physics of the very early Universe.« less

title: Primordial Non-Gaussianities and Zero-Bias Tracers of the Large-Scale Structure.
abstract: We develop a new method to constrain primordial non-Gaussianities of the local kind using unclustered tracers of the large scale structure. We show that, in the limit of low noise, zero bias tracers yield large improvement over standard methods, mostly due to vanishing sampling variance. We propose a simple technique to construct such a tracer, using environmental information obtained from the original sample and validate our method with N-body simulations. Our results indicate that σ_{f_{NL}^{loc}}≃1 can be reached using only information on a single tracer of sufficiently high number density.

title: The clustering of galaxies in the SDSS-III DR9 Baryon Oscillation Spectroscopic Survey: constraints
abstract: We analyse the density field of 264 283 galaxies observed by the Sloan Digital Sky Surve (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) and included in the SDSS Data Release 9 (DR9). In total, the SDSS DR9 BOSS data include spectroscopic redshifts for over 400 000 galaxies spread over a footprint of more than 3000 deg^2. We measure the power spectrum of these galaxies with redshifts 0.43 0), is 99.5 per cent. After quantifying and correcting for the systematic bias 
and including the added uncertainty, we find −45 0) = 91.0 per cent. A more conservative approach assumes that we have only learnt the k dependence of the systematic bias and allows any amplitude for the systematic correction; we find that the systematic effect is not fully degenerate with that of f^(local)_(NL) , and we determine that −82 0) = 68 per cent. This analysis demonstrates the importance of accounting for the impact of Galactic foregrounds on f^(local)_(NL) measurements. We outline the methods that account for these systematic biases and uncertainties. We expect our methods to yield robust constraints on f^(local)_(NL) for both our own and future large-scale structure investigations.

title: Improved Primordial Non-Gaussianity Constraints from Measurements of Galaxy Clustering and the Integrated Sachs-Wolfe Effect
abstract: We present the strongest robust constraints on primordial non-Gaussianity (PNG) from currently available galaxy surveys, combining large-scale clustering measurements and their cross correlations with the cosmic microwave background. We update the data sets used by Giannantonio et al. (2012), and broaden that analysis to include the full set of two-point correlation functions between all surveys. In order to obtain the most reliable constraints on PNG, we advocate the use of the cross correlations between the catalogs as a robust estimator and we perform an extended analysis of the possible systematics to reduce their impact on the results. To minimize the impact of stellar contamination in our luminous red galaxy sample, we use the recent Baryon Oscillations Spectroscopic Survey catalog of Ross et al. (2011). We also find evidence for a new systematic in the NVSS radio galaxy survey similar to, but smaller than, the known declination-dependent issue; this is difficult to remove without affecting the inferred PNG signal, and thus we do not include the NVSS autocorrelation function in our analyses. We find no evidence of primordial non-Gaussianity; for the local-type configuration we obtain for the skewness parameter −36

title: Constraints on Primordial Non-Gaussianity from 800 000 Photometric Quasars.
abstract: We derive robust constraints on primordial non-Gaussianity (PNG) using the clustering of 800 000 photometric quasars from the Sloan Digital Sky Survey in the redshift range 0.5<z<3.5. These measurements rely on the novel technique of extended mode projection to control the impact of spatially varying systematics in a robust fashion, making use of blind analysis techniques. This allows the accurate measurement of quasar halo bias at the largest scales, while discarding as little as possible of the data. The standard local-type PNG parameters f_{NL} and g_{NL} both imprint a k^{-2} scale-dependent effect in the bias. Constraining these individually, we obtain -49<f_{NL}<31 and -2.7×10^{5}<g_{NL}<1.9×10^{5}, while their joint constraints lead to -105<f_{NL}<72 and -4.0×10^{5}<g_{NL}<4.9×10^{5} (all at 95% C.L.). Introducing a running parameter n_{f_{NL}} to constrain b(k)∝k^{-2+n_{f_{NL}}} and a generalized PNG amplitude f[over ˜]_{NL}, we obtain -45.5 exp(3.7n_{f_{NL}})<f[over ˜]_{NL}<34.4 exp(3.3n_{f_{NL}}) at 95% C.L. These results incorporate uncertainties in the cosmological parameters, redshift distributions, shot noise, and the bias prescription used to relate the quasar clustering to the underlying dark matter. These are the strongest constraints obtained to date on PNG using a single population of large-scale structure tracers, and are already at the level of pre-Planck constraints from the cosmic microwave background. A conservative forecast for a Large Synoptic Survey Telescope (LSST)-like survey incorporating mode projection yields σ(f_{NL})∼5-competitive with the Planck result-highlighting the power of upcoming large scale structure surveys to probe the initial conditions of the Universe.

title: Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
abstract: We present the final nine-year maps and basic results from the Wilkinson Microwave Anisotropy Probe (WMAP) mission. The full nine-year analysis of the time-ordered data provides updated characterizations and calibrations of the experiment. We also provide new nine-year full sky temperature maps that were processed to reduce the asymmetry of the effective beams. Temperature and polarization sky maps are examined to separate cosmic microwave background (CMB) anisotropy from foreground emission, and both types of signals are analyzed in detail. We provide new point source catalogs as well as new diffuse and point source foreground masks. An updated template-removal process is used for cosmological analysis; new foreground fits are performed, and new foreground-reduced CMB maps are presented. We now implement an optimal C ?1 weighting to compute the temperature angular power spectrum. The WMAP mission has resulted in a highly constrained ?CDM cosmological model with precise and accurate parameters in agreement with a host of other cosmological measurements. When WMAP data are combined with finer scale CMB, baryon acoustic oscillation, and Hubble constant measurements, we find that big bang nucleosynthesis is well supported and there is no compelling evidence for a non-standard number of neutrino species (N eff = 3.84 ? 0.40). The model fit also implies that the age of the universe is t 0 = 13.772 ? 0.059 Gyr, and the fit Hubble constant is H 0 = 69.32 ? 0.80?km?s?1?Mpc?1. Inflation is also supported: the fluctuations are adiabatic, with Gaussian random phases; the detection of a deviation of the scalar spectral index from unity, reported earlier by the WMAP team, now has high statistical significance (ns = 0.9608 ? 0.0080); and the universe is close to flat/Euclidean (). Overall, the WMAP mission has resulted in a reduction of the cosmological parameter volume by a factor of 68,000 for the standard six-parameter ?CDM model, based on CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor 117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces the cosmological parameter volume even further. With no significant anomalies and an adequate goodness of fit, the inflationary flat ?CDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology.

title: Search for primordial non-Gaussianity in the quasars of SDSS-III BOSS DR9
abstract: We analyse the clustering of 22 361 quasars between redshift 2.2 < z < 2.9 observed with the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS), which are included in the ninth data release (DR9). We fit the clustering results with a Λcold dark matter (ΛCDM) model to calculate the linear bias of the quasar sample, b = 3.74 ± 0.12. The measured value of bias is consistent with the findings of White et al., where they analyse almost the same quasar sample, although only in the range s < 40 h−1 Mpc. At large scales we observe an excess or plateau in the clustering correlation function. By fitting a model that incorporates a scale dependent additional term in the bias introduced by primordial non-Gaussianity of the local type, we calculate the amplitude of the deviation from the Gaussian initial conditions as 70 < fNLlocal < 190 at the 95 per cent confidence level. We correct the sample from systematics according to the methods of Ross et al. and Ho et al., with the fNLlocal measurements after the application of the two methods being consistent with each other. Finally, we use cross-correlations across redshift slices to test the corrected sample for any remaining unknown sources of systematics, but the results give no indication of any such further errors. We consider as our final results on non-Gaussianity, 46 < fNLlocal < 158 at 95 per cent confidence, after correcting the sample with the weights method of Ross et al. These results are consistent with previous tight constraints on non-Gaussianity from other Large-Scale Structures surveys, but are in tension with the latest results from the cosmic microwave background.

title: The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: analysis of potential systematics
abstract: We analyse the density field of galaxies observed by the Sloan Digital Sky Survey (SDSS)-III Baryon Oscillation Spectroscopic Survey (BOSS) included in the SDSS Data Release Nine (DR9). DR9 includes spectroscopic redshifts for over 400 000 galaxies spread over a footprint of 3275 deg2. We identify, characterize and mitigate the impact of sources of systematic uncertainty on large-scale clustering measurements, both for angular moments of the redshift-space correlation function, ξl(s), and the spherically averaged power spectrum, P(k), in order to ensure that robust cosmological constraints will be obtained from these data. A correlation between the projected density of stars and the higher redshift (0.43 120 h−1 Mpc or k < 0.01 h Mpc−1. We find that these errors can be ameliorated by weighting galaxies based on their surface brightness and the local stellar density. The clustering of CMASS galaxies found in the Northern and Southern Galactic footprints of the survey generally agrees to within 2σ. We use mock galaxy catalogues that simulate the CMASS selection function to determine that randomly selecting galaxy redshifts in order to simulate the radial selection function of a random sample imparts the least systematic error on ξl(s) measurements and that this systematic error is negligible for the spherically averaged correlation function, ξ0. We find a peak in ξ0 at s~ 200 h−1 Mpc, with a corresponding feature with period ~0.03 h Mpc−1 in P(k), and find features at least as strong in 4.8 per cent of the mock galaxy catalogues, concluding this feature is likely to be a consequence of cosmic variance. The methods we recommend for the calculation of clustering measurements using the CMASS sample are adopted in companion papers that locate the position of the baryon acoustic oscillation feature, constrain cosmological models using the full shape of ξ0 and measure the rate of structure growth.

title: Systematic Effects in Large-Scale Angular Power Spectra of Photometric Quasars and Implications for Constraining Primordial Non-Gaussianity
abstract: Primordial non-Gaussianity of local type is predicted to lead to enhanced halo clustering on very large scales. Photometric quasars, which can be seen from cosmological redshifts z > 2 even in wide-shallow optical surveys, are promising tracers for constraining non-Gaussianity using this effect. However, large-scale systematics can also mimic this signature of non-Gaussianity. In order to assess the contribution of systematic effects, we cross-correlate overdensity maps of photometric quasars from the Sloan Digital Sky Survey (SDSS) Data Release 6 (DR6) in different redshift ranges. We find that the maps are significantly correlated on large scales, even though we expect the angular distributions of quasars at different redshifts to be uncorrelated. This implies that the quasar maps are contaminated with systematic errors. We investigate the use of external templates that provide information on the spatial dependence of potential systematic errors to reduce the level of spurious clustering in the quasar data. We find that templates associated with stellar density, the stellar color locus, airmass, and seeing are major contaminants of the quasar maps, with seeing having the largest effect. Using template projection, we are able to decrease the significance of the cross-correlation measurement on the largest scales from 9.2σ to 5.4σ. Although this is an improvement, the remaining cross-correlation suggests the contamination in this quasar sample is too great to allow a competitive constraint on f_NL by correlations internal to this sample. The SDSS quasar catalog exhibits spurious number density fluctuations of approximately 2% rms, and we need a contamination level less than 1% (0.6%) in order to measure values of f_NL less than 100 (10). Properly dealing with these systematics will be paramount for future large scale structure surveys that seek to constrain non-Gaussianity.

title: Estimating the large-scale angular power spectrum in the presence of systematics: a case study of Sloan Digital Sky Survey quasars
abstract: The angular power spectrum is a powerful statistic for analysing cosmological signals imprinted in the clustering of matter. However, current galaxy and quasar surveys cover limited portions of the sky, and are contaminated by systematics that can mimic cosmological signatures and jeopardise the interpretation of the measured power spectra. We provide a framework for obtaining unbiased estimates of the angular power spectra of large-scale structure surveys at the largest scales using quadratic estimators. The method is tested by analysing the 600 CMASS mock catalogues constructed by Manera et al. (2013) for the Baryon Oscillation Spectroscopic Survey (BOSS). We then consider the Richards et al. (2009) catalogue of photometric quasars from the Sixth Data Release (DR6) of the Sloan Digital Sky Survey (SDSS), which is known to include significant stellar contamination and systematic uncertainties. Focusing on the sample of ultraviolet-excess (UVX) sources, we show that the excess clustering power present on the largest-scales can be largely mitigated by making use of improved sky masks and projecting out the modes corresponding to the principal systematics. In particular, we find that the sample of objects with photometric redshift $1.3 < z_p < 2.2$ exhibits no evidence of contamination when using our most conservative mask and mode projection. This indicates that any residual systematics are well within the statistical uncertainties. We conclude that, using our approach, this sample can be used for cosmological studies.

title: Exploiting the full potential of photometric quasar surveys: Optimal power spectra through blind mitigation of systematics
abstract: We present optimal measurements of the angular power spectrum of the XDQSOz catalogue of photometric quasars from the Sloan Digital Sky Survey. These measurements rely on a quadratic maximum likelihood estimator that simultaneously measures the auto- and cross-power spectra of four redshift samples, and provides minimum-variance, unbiased estimates even at the largest angular scales. Since photometric quasars are known to be strongly affected by systematics such as spatially-varying depth and stellar contamination, we introduce a new framework of extended mode projection to robustly mitigate the impact of systematics on the power spectrum measurements. This technique involves constructing template maps of potential systematics, decorrelating them on the sky, and projecting out modes which are significantly correlated with the data. Our method is able to simultaneously process several thousands of nonlinearly-correlated systematics, and mode projection is performed in a blind fashion. Using our final power spectrum measurements, we find a good agreement with theoretical predictions, and no evidence for further contamination by systematics. Extended mode projection not only obviates the need for aggressive sky and quality cuts, but also provides control over the level of systematics in the measurements, enabling the search for small signals of new physics while avoiding confirmation bias.

title: A map-based method for eliminating systematic modes from galaxy clustering power spectra with application to BOSS
abstract: We develop a practical methodology to remove modes from a galaxy survey power spectrum that are associated with systematic errors. We apply this to the BOSS CMASS sample, to see if it removes the excess power previously observed beyond the best-fit $\Lambda$CDM model on very large scales. We consider several possible sources of data contamination, and check whether they affect the number of targets that can be observed and the power spectrum measurements. We describe a general framework for how such knowledge can be transformed into template fields. Mode subtraction can then be used to remove these systematic contaminants at least as well as applying corrective weighting to the observed galaxies, but benefits from giving an unbiased power. Even after applying templates for all known systematics, we find a large-scale power excess, but this is reduced compared with that observed using the weights provided by the BOSS team. This excess is at much larger scales than the BAO scale and does not affect the main results of BOSS. However, it will be important for the measurement of a scale-dependent bias due to primordial non-Gaussianity. The excess is beyond that allowed by any simple model of non-Gaussianity matching Planck data, and is not matched in other surveys. We show that this power excess can further be reduced but is still present using "phenomenological" templates, designed to consider further potentially unknown sources of systematic contamination. As all discrepant angular modes can be removed using "phenomenological" templates, the potentially remaining contaminant acts radially.

title: Parameter constraints from cross-correlation of CMB lensing with galaxy clustering
abstract: The lensing convergence measurable with future CMB surveys like CMB-S4 will be highly correlated with the clustering observed by deep photometric large scale structure (LSS) surveys such as the LSST, with cross-correlation coefficient as high as 95\%. This will enable use of sample variance cancellation techniques to determine cosmological parameters, and use of cross-correlation measurements to break parameter degeneracies. Assuming large sky overlap between CMB-S4 and LSST, we show that a joint analysis of CMB-S4 lensing and LSST clustering can yield very tight constraints on the matter amplitude $\sigma_8(z)$, halo bias, and $f_\mathrm{NL}$, competitive with the best stage IV experiment predictions, but using complementary methods, which may carry different and possibly lower systematics. Having no sky overlap between experiments degrades the precision of $\sigma_8(z)$ by a factor of 20, and that of $f_\mathrm{NL}$ by a factor of 1.5 to 2. Without CMB lensing, the precision always degrades by an order of magnitude or more, showing that a joint analysis is critical. Our results also suggest that CMB lensing in combination with LSS photometric surveys is a competitive probe of the evolution of structure in the redshift range $z\simeq 1-7$, probing a regime that is not well tested observationally. We explore predictions against other surveys and experiment configurations, finding that wide patches with maximal sky overlap between CMB and LSS surveys are most powerful for $\sigma_8(z)$ and $f_\mathrm{NL}$.

title: Optimal redshift weighting for baryon acoustic oscillations
abstract: ; Padmanabhan, N; White, M |  Future baryon acoustic oscillation (BAO) surveys will survey very large volumes, covering wide ranges in redshift. We derive a set of redshift weights to compress the information in the redshift direction to a small number of modes. We suggest that such a compression preserves almost all of the signal for most cosmologies, while giving high signal-to-noise measurements for each combination. We present some toy models and simple worked examples. As an intermediate step, we give a precise meaning to the 'effective redshift' of a BAO measurement.

title: Redshift weights for baryon acoustic oscillations: Application to mock galaxy catalogues
abstract: ; Padmanabhan, N; White, M; Ross, AJ; Zhao, G |  Large redshift surveys capable of measuring the baryon acoustic oscillation (BAO) signal have proven to be an effective way of measuring the distance-redshift relation in cosmology. Building off the work in Zhu et al., we develop a technique to directly constrain the distance- redshift relation from BAO measurements without splitting the sample into redshift bins. We apply the redshift weighting technique in Zhu et al. to the clustering of galaxies from 1000 Quick particle mesh (QPM) mock simulations after reconstruction and achieve a 0.75 per cent measurement of the angular diameter distance DA at z = 0.64 and the same precision for Hubble parameter H at z = 0.29. These QPM mock catalogues mimic the clustering and noise level of the Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12). We compress the correlation functions in the redshift direction on to a set of weighted correlation functions. These estimators give unbiased DA and H measurements across the entire redshift range of the combined sample. We demonstrate the effectiveness of redshift weighting in improving the distance and Hubble parameter estimates. Instead of measuring at a single 'effective' redshift as in traditional analyses, we report our DA and H measurements at all redshifts. The measured fractional error of DA ranges from 1.53 per cent at z = 0.2 to 0.75 per cent at z = 0.64. The fractional error of H ranges from 0.75 per cent at z = 0.29 to 2.45 per cent at z = 0.7. Our measurements are consistent with a Fisher forecast to within 10-20 per cent depending on the pivot redshift.We further showthe results are robust against the choice of fiducial cosmologies, galaxy bias models, and redshift-space distortions streaming parameters.

title: Optimal redshift weighting for redshift-space distortions
abstract: The low-statistical errors on cosmological parameters promised by future galaxy surveys will only be realized with the development of new, fast, analysis methods that reduce potential systematic problems to low levels. We present an efficient method for measuring the evolution of the growth of structure using redshift-space distortions (RSDs), that removes the need to make measurements in redshift shells. We provide sets of galaxy-weights that cover a wide range in redshift, but are optimized to provide differential information about cosmological evolution. These are derived to optimally measure the coefficients of a parametrization of the redshift-dependent matter density, which provides a framework to measure deviations from the concordance ΛCDM cosmology, allowing for deviations in both geometric and/or growth. We test the robustness of the weights by comparing with alternative schemes and investigate the impact of galaxy bias. We extend the results to measure the combined anisotropic baryon acoustic oscillation and RSD signals.

title: The SDSS-IV extended baryon oscillation spectroscopic survey: Overview and early data
abstract: In a six-year program started in 2014 July, the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) will conduct novel cosmological observations using the BOSS spectrograph at Apache Point Observatory. These observations will be conducted simultaneously with the Time Domain Spectroscopic Survey (TDSS) designed for variability studies and the Spectroscopic Identification of eROSITA Sources (SPIDERS) program designed for studies of X-ray sources. In particular, eBOSS will measure with percent-level precision the distance-redshift relation with baryon acoustic oscillations (BAO) in the clustering of matter. eBOSS will use four different tracers of the underlying matter density field to vastly expand the volume covered by BOSS and map the large-scale-structures over the relatively unconstrained redshift range 0.6 0.6 sample of BOSS galaxies. With ~195,000 new emission line galaxy redshifts, we expect BAO measurements of d_A(z) to an accuracy of 3.1% and H(z) to 4.7% at an effective redshift of z = 0.87. A sample of more than 500,000 spectroscopically confirmed quasars will provide the first BAO distance measurements over the redshift range 0.9 2.1; these new data will enhance the precision of dA(z) and H(z) at z > 2.1 by a factor of 1.44 relative to BOSS. Furthermore, eBOSS will provide improved tests of General Relativity on cosmological scales through redshift-space distortion measurements, improved tests for non-Gaussianity in the primordial density field, and new constraints on the summed mass of all neutrino species. Here, we provide an overview of the cosmological goals, spectroscopic target sample, demonstration of spectral quality from early data, and projected cosmological constraints from eBOSS.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measuring the evolution of the growth rate using redshift-space distortions between redshift 0.8 and 2.2
abstract: We measure the growth rate and its evolution using the anisotropic clustering of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample, which includes |$148\, 659$| quasars covering the wide redshift range of 0.8 < z < 2.2 and a sky area of |$2112.90\, \rm deg^2$|⁠. To optimize measurements we deploy a redshift-dependent weighting scheme, which allows us to avoid binning and perform the data analysis consistently including the redshift evolution across the sample. We perform the analysis in Fourier space, and use the redshift evolving power spectrum multipoles to measure the redshift-space distortion parameter fσ_8 and parameters controlling the anisotropic projection of the cosmological perturbations. We measure fσ_8(z = 1.52) = 0.43 ± 0.05 and dfσ_8/dz(z = 1.52) = −0.16 ± 0.08, consistent with the expectation for a lambda cold dark matter cosmology as constrained by the Planck experiment.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: Measuring the anisotropic baryon acoustic oscillations with redshift weights
abstract: ; Padmanabhan, N; Ross, AJ; White, M; Percival, WJ; Ruggeri, R; Zhao, GB; Wang, D; Mueller, EM; Burtin, E; Gil-Marin, H; Bautista, J; Beutler, F; Brinkmann, J; Brownstein, JR; Dawson, K; Macorra, ADL; Rossi, G; Schneider, DP; Tojeiro, R; Wang, Y |  We present an anisotropic analysis of baryon acoustic oscillation (BAO) signal from the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample. The sample consists of 147 000 quasars distributed over a redshift range of 0.8 l z l 2.2. We apply the redshift weights technique to the clustering of quasars in this sample and achieve a 4.6 per cent measurement of the angular distance measurement DM at z = 2.2 and Hubble parameter H at z = 0.8. We parametrize the distance-redshift relation, relative to a fiducial model, as a Taylor series. The coefficients of this expansion are used to reconstruct the distance-redshift relation and obtain distance and Hubble parameter measurements at all redshifts within the redshift range of the sample. Reporting the result at two characteristic redshifts, we determine DM(z = 1) = 3405 ± 305 (rd/rd, fid)Mpc, H(z = 1) = 120.7 ± 7.3 (rd, fid/rd) kms-1 Mpc-1 andDM(z=2)=5325±249 (rd/rd, fid)Mpc, H(z = 2) = 189.9 ± 32.9 (rd, fid/rd) km s-1 Mpc-1. These measurements are highly correlated. We assess the outlook of BAO analysis from the final quasar sample by testing the method on a set of mocks that mimic the noise level in the final sample. We demonstrate on these mocks that redshift weighting shrinks the measurement error by over 25 per cent on average. We conclude redshift weighting can bring us closer to the cosmological goal of the final quasar sample.

title: The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space
abstract: We perform a tomographic baryon acoustic oscillations (BAOs) analysis using the two-point galaxy correlation function measured from the combined sample of Baryon Oscillation Spectroscopic Survey Data Release 12 (BOSS DR12), which covers the redshift range of 0.2 < z < 0.75. Upon splitting the sample into multiple overlapping redshift slices to extract the redshift information of galaxy clustering, we obtain a measurement of D-A(z)/r(d) and H(z)r(d) at nine effective redshifts with the full covariance matrix calibrated using MultiDark-Patchy mock catalogues. Using the reconstructed galaxy catalogues, we obtain the precision of 1.3-2.2 per cent for D-A(z)/r(d) and 2.1-6.0 per cent for H(z)r(d.) To quantify the gain from the tomographic information, we compare the constraints on the cosmological parameters using our nine-bin BAO measurements, the consensus three-bin BAO and redshift space distortion measurements at three effective redshifts in Alam et al., and the non-tomographic (one-bin) BAO measurement at a single effective redshift. Comparing the nine-bin with one-bin constraint result, it can improve the dark energy Figure of Merit by a factor of 1.24 for the Chevallier-Polarski-Linder parametrization for equation-of-state parameter w(DE). The errors of w(0) and w(a) from nine-bin constraints are slightly improved when compared to the three-bin constraint result.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measurement of the growth rate of structure from the anisotropic correlation function between redshift 0.8 and 2.2
abstract: PZ and EB acknowledge support from the P2IO LabEx (reference ANR-10-LABX-0038). HGM acknowledges support from the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received financial state aid managed by the Agence Nationalede la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02. AJR is grateful for support from the Ohio State University Center for Cosmology and ParticlePhysics. GBZ is supported by NSFC Grants 1171001024 and 11673025. GBZ is also supported by a Royal Society Newton Advanced Fellowship, hosted by University of Portsmouth. SH's and KH's work was supported under the U.S. Department of Energy contract DE-AC02-06CH11357. GBZ is supported by NSFC Grant No. 11673025, and by a Royal Society Newton Advanced Fellowship. GR acknowledges support from the National Research Foundation of Korea (NRF) through Grant No. 2017077508 funded by the Korean Ministry of Education, Science and Technology (MoEST), and from the faculty research fund of Sejong University in 2018. Funding for SDSS-III and SDSS-IV has been provided by the Alfred P. Sloan Foundation and Participating Institutions. Additional funding for SDSS-III comes from the National Science Foundation and the U.S. Department of Energy Office of Science. Further information about both projects is available at www.sdss.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions in both collaborations. In SDSS-III, these include the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. The Participating Institutions in SDSS-IV are CarnegieMellon University, Colorado University, Boulder, Harvard-Smithsonian Center for Astrophysics Participation Group, Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe Max-Planck-Institut fuer Astrophysik (MPA Garching), Max-Planck-Institut fuer Extraterrestrische Physik (MPE), Max-Planck-Institut fuer Astronomie (MPIA Heidelberg), National Astronomical Observatories of China, New Mexico State University, New York University, The Ohio State University, Penn State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, University of Portsmouth, University of Utah, University of Wisconsin, and Yale University. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under contract DE-AC02-06CH11357. This work made use of the facilities and staff of the UK Sciama High Performance Computing cluster supported by the ICG, SEPNet, and the University of Portsmouth. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No.r DE-AC02-05CH11231.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: anisotropic Baryon Acoustic Oscillations measurements in Fourier-space with optimal redshift weights
abstract: We present a measurement of the anisotropic and isotropic Baryon Acoustic Oscillations (BAO) from the extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample with optimal redshift weights. Applying the redshift weights improves the constraint on the BAO dilation parameter α(z_eff) by 17 per cent. We reconstruct the evolution history of the BAO distance indicators in the redshift range of 0.8 < z < 2.2. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

title: Optimizing primordial non-Gaussianity measurements from galaxy surveys
abstract: Galaxy clustering data from current and upcoming large scale structure surveys can provide strong constraints on primordial non-Gaussianity through the scale-dependent halo bias. To fully exploit the information from galaxy surveys, optimal analysis methods need to be developed and applied to the data. Since the halo bias is sensitive to local non-Gaussianity predominately at large scales, the volume of a given survey is crucial. Consequently, for such analyses we do not want to split into redshift bins, which would lead to information loss due to edge effects, but instead analyse the full sample. We present an optimal technique to directly constrain local non-Gaussianity parametrised by $f_\mathrm{NL}^\mathrm{loc}$, from galaxy clustering by applying redshift weights to the galaxies. We derive a set of weights to optimally measure the amplitude of local non-Gaussianity, $f_\mathrm{NL}^\mathrm{loc}$, discuss the redshift weighted power spectrum estimators, outline the implementation procedure and test our weighting scheme against Lognormal catalogs for two different surveys: the quasar sample of the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) and the emission line galaxy sample of the Dark Energy Spectroscopic Instrument (DESI) survey. We find an improvement of 30 percent for eBOSS and 6 percent for DESI compared to the standard Feldman, Kaiser $\&$ Peacock weights, although these predictions are sensitive to the bias model assumed.

title: Power spectrum analysis of three-dimensional redshift surveys
abstract: We develop a general method for power spectrum analysis of three dimensional redshift surveys. We present rigorous analytical estimates for the statistical uncertainty in the power and we are able to derive a rigorous optimal weighting scheme under the reasonable (and largely empirically verified) assumption that the long wavelength Fourier components are Gaussian distributed. We apply the formalism to the updated 1-in-6 QDOT IRAS redshift survey, and compare our results to data from other probes: APM angular correlations; the CfA and the Berkeley 1.2Jy IRAS redshift surveys. Our results bear out and further quantify the impression from e.g.\ counts-in-cells analysis that there is extra power on large scales as compared to the standard CDM model with $\Omega h\simeq 0.5$. We apply likelihood analysis using the CDM spectrum with $\Omega h$ as a free parameter as a phenomenological family of models; we find the best fitting parameters in redshift space and transform the results to real space. Finally, we calculate the distribution of the estimated long wavelength power. This agrees remarkably well with the exponential distribution expected for Gaussian fluctuations, even out to powers of ten times the mean. Our results thus reveal no trace of periodicity or other non-Gaussian behavior.

title: The Fourteenth Data Release of the Sloan Digital Sky Survey: First Spectroscopic data from the extended Baryon Oscillation Spectroscopic Survey and from the second phase of the Apache Point Observatory Galactic Evolution Experiment
abstract: The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since 2014 July. This paper describes the second data release from this phase, and the 14th from SDSS overall (making this Data Release Fourteen or DR14). This release makes the data taken by SDSS-IV in its first two years of operation (2014–2016 July) public. Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey; the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data-driven machine-learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from the SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS web site (www.sdss.org) has been updated for this release and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020 and will be followed by SDSS-V.

title: Verifying the consistency relation for the scale-dependent bias from local primordial non-Gaussianity
abstract: We measure the large-scale bias of dark matter haloes in simulations with non-Gaussian initial conditions of the local type, and compare this bias to the response of the mass function to a change in the primordial amplitude of fluctuations. The two are found to be consistent, as expected from physical arguments, for the three halo-finder algorithms which use different spherical overdensity (SO) and friends-of-friends methods. On the other hand, we find that the commonly used prediction for universal mass functions, that the scale-dependent bias is proportional to the first-order Gaussian Lagrangian bias, does not yield a good agreement with the measurements. For all halo finders, high-mass haloes show a non-Gaussian bias suppressed by 10-15 per cent relative to the universal mass function prediction. For SO haloes, this deviation changes sign at low masses, where the non-Gaussian bias becomes larger than the universal prediction.

title: Non-Gaussian halo assembly bias
abstract: The strong dependence of the large-scale dark matter halo bias on the (local) non-Gaussianity parameter, fNL, 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.

title: How to measure CMB power spectra without losing information
abstract: A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties: 
(1) It is unbeatable in the sense that no other method can measure C_l with smaller error bars. 
(2) It is quadratic, which makes the statistical properties of the measurements easy to compute and use for estimation of cosmological parameters. 
(3) It is computationally faster than rival high-precision methods such as the nonlinear maximum-likelihood technique, with the crucial steps scaling as n^2 rather than n^3, where n is the number of map pixels. 
(4) It is applicable to any survey geometry whatsoever, with arbitraty regions masked out and arbitrary noise behaviour. 
(5) It is not a "black-box" method, but quite simple to understand intuitively: it corresponds to a high-pass filtering and edge softening of the original map followed by a straight expansion in truncated spherical-harmonics. 
It is argued that this method is computationally feasible even for futute high-resolution CMB experiments with n=10^6-10^7. It is also shown that C_l computed with this method is useful not merely for graphical presentation purposes, but also as an intermediate (and arguably necessary) step in the data analysis pipeline, reducing the data set to a more manageable size before the final step of constraining Gaussian cosmological models and parameters - while retaining all the cosmological information that was present in the original map.

title: 2 1 A pr 2 00 0 Radical Compression of Cosmic Microwave Background Data
abstract: Powerful constraints on theories can already be inferred from existing CMB anisotropy data. But performing an exact analysis of available data is a complicated task and may become prohibitively so for upcoming experiments with & 10 pixels. We present a method for approximating the likelihood that takes power spectrum constraints, e.g., “band-powers”, as inputs. We identify a bias which results if one approximates the probability distribution of the band-power errors as Gaussian—as is the usual practice. This bias can be eliminated by using specific approximations to the non-Gaussian form for the distribution specified by three parameters (the maximum likelihood or mode, curvature or variance, and a third quantity). We advocate the calculation of this third quantity by experimenters, to be presented along with the maximum-likelihood band-power and variance. We use this non-Gaussian form to estimate the power spectrum of the CMB in eleven bands from multipole moment l = 2 (the quadrupole) to l = 3000 from all published band-power data. We investigate the robustness of our power spectrum estimate to changes in these approximations as well as to selective editing of the data.  data analysis — methods: statistical

title: Measuring Cosmological Parameters with Galaxy Surveys
abstract: We assess the accuracy with which future galaxy surveys can measure cosmological parameters. By breaking parameter degeneracies of the Planck cosmic microwave background satellite, the Sloan digital sky survey may be able to reduce the Planck error bars by about an order of magnitude on the large-scale power normalization and the reionization optical depth, down to percent levels. However, pinpointing attainable accuracies to within better than a factor of a few depends crucially on whether it will be possible to extract useful information from the mildly nonlinear regime.

title: Measuring the galaxy power spectrum with future redshift surveys
abstract: Precision measurements of the galaxy power spectrum P(k) require a data analysis pipeline that is both fast enough to be computationally feasible and accurate enough to take full advantage of high-quality data. We present a rigorous discussion of different methods of power spectrum estimation, with emphasis on the traditional Fourier method and linear (Karhunen-Loeve; KL) and quadratic data compression schemes, showing in what approximations they give the same result. To improve speed, we show how many of the advantages of KL data compression and power spectrum estimation may be achieved with a computationally faster quadratic method. To improve accuracy, we derive analytic expressions for handling the integral constraint, since it is crucial that finite volume effects are accurately corrected for on scales comparable to the depth of the survey. We also show that for the KL and quadratic techniques, multiple constraints can be included via simple matrix operations, thereby rendering the results less sensitive to Galactic extinction and misestimates of the radial selection function. We present a data analysis pipeline that we argue does justice to the increases in both quality and quantity of data that upcoming redshift surveys will provide. It uses three analysis techniques in conjunction: a traditional Fourier approach on small scales, a pixelized quadratic matrix method on large scales, and a pixelized KL eigenmode analysis to probe anisotropic effects such as redshift-space distortions.

title: A Measurement of the Quadrupole Power Spectrum in the Clustering of the 2dF QSO Survey
abstract: We report on a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis used an algorithm parallel to that for estimating the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum was rather large, but the best-fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.

title: Measuring line-of-sight-dependent Fourier-space clustering using FFTs
abstract: Observed galaxy clustering exhibits local transverse statistical isotropy around the lineof-sight (LOS). The variation of the LOS across a galaxy survey complicates the measurement of the observed clustering as a function of the angle to the LOS, as fast Fourier transforms (FFTs) based on Cartesian grids, cannot individually allow for this. Recent advances in methodology for calculating LOS-dependent clustering in Fourier space include the realization that power spectrum LOS-dependent moments can be constructed from sums over galaxies, based on approximating the LOS to each pair of galaxies by the LOS to one of them. We show that we can implement this method using multiple FFTs, each measuring the LOS-weighted clustering along different axes. The N logN nature of FFTs means that the computational speed-up is a factor of > 1000 compared with summing over galaxies. This development should be beneficial for future projects such as DESI and Euclid which will provide an order of magnitude more galaxies than current surveys.

title: Fast estimators for redshift-space clustering
abstract: Redshift-space distortions in galaxy surveys happen along the radial direction, breaking statistical translation invariance. We construct estimators for radial distortions that, using only Fast Fourier Transforms (FFTs) of the overdensity field multipoles for a given survey geometry, compute the power spectrum monopole, quadrupole and hexadecapole, and generalize such estimators to the bispectrum. Using realistic mock catalogs we compare the signal to noise of two estimators for the power spectrum hexadecapole that require different number of FFTs and measure the bispectrum monopole, quadrupole and hexadecapole. The resulting algorithm is very efficient, e.g. for the BOSS survey requires about three minutes for $\ell=0,2,4$ power spectra for scales up to $k=0.3~h/$Mpc and about fifteen additional minutes for $\ell=0,2,4$ bispectra for all scales and triangle shapes up to $k=0.2~h/$Mpc on a single core. The speed of these estimators is essential as it makes possible to compute covariance matrices from large number of realizations of mock catalogs with realistic survey characteristics, and paves the way for improved constrains of gravity on cosmological scales, inflation and galaxy bias.

title: An optimal FFT-based anisotropic power spectrum estimator
abstract: Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. Consequently, our method is substantially faster: a given multipole of order $\ell$ requires only $2\ell+1$ FFTs rather than the $(\ell+1)(\ell+2)/2$ FFTs of the Cartesian approach. For the hexadecapole ($\ell = 4$), this translates to $40\%$ fewer FFTs, with increased savings for higher $\ell$. The reduction in wall-clock time enables the calculation of finely-binned wedges in $P(k,\mu)$, obtained by computing multipoles up to a large $\ell_{\rm max}$ and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in $\mu$, we can isolate plane-of-sky (angular) systematics to a narrow bin at $\mu \simeq 0$ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in $\mu$ becomes ill-conditioned when combining multipoles up to large values of $\ell_{\rm max}$, but that the problem can be avoided with non-uniform binning. As an example, we present results using $\ell_{\rm max}=16$, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first $\mu$ bin leads only to a 7% increase in statistical error on $f \sigma_8$, as compared to a 54% increase with $\ell_{\rm max}=4$.

title: Interpreting measurements of the anisotropic galaxy power spectrum
abstract: The most commonly used estimators of the anisotropic galaxy power spectrum employ Fast Fourier transforms, and rely on a specific choice of the line-of-sight that breaks the symmetry between the galaxy pair. This leads to wide-angle effects, including the presence of odd power spectrum multipoles like the dipole ($\ell = 1$) and octopole ($\ell = 3$). In Fourier-space these wide-angle effects also couple to the survey window function. We present a self-consistent framework extending the commonly used window function treatment to include the wide-angle effects. We show that our framework can successfully model the wide-angle effects in the BOSS DR12 dataset. We present estimators for the odd power spectrum multipoles and, detect these multipoles in BOSS DR12 with high significance. Understanding the impact of the wide-angle effects on the power spectrum multipoles is essential for many cosmological observables like primordial non-Gaussianity and the detection of General Relativistic effects and represents a potential systematic for measurements of Baryon Acoustic Oscillations and redshift-space distortions.

title: The 2.5 m Telescope of the Sloan Digital Sky Survey
abstract: We describe the design, construction, and performance of the Sloan Digital Sky Survey telescope located at Apache Point Observatory. The telescope is a modified two-corrector Ritchey-Chretien design with a 2.5 m, f/2.25 primary, a 1.08 m secondary, a Gascoigne astigmatism corrector, and one of a pair of interchangeable highly aspheric correctors near the focal plane, one for imaging and the other for spectroscopy. The final focal ratio is f/5. The telescope is instrumented by a wide-area, multiband CCD camera and a pair of fiber-fed double spectrographs. Novel features of the telescope include the following: (1) A 3° diameter (0.65 m) focal plane that has excellent image quality and small geometric distortions over a wide wavelength range (3000-10,600 A) in the imaging mode, and good image quality combined with very small lateral and longitudinal color errors in the spectroscopic mode. The unusual requirement of very low distortion is set by the demands of time-delay-and-integrate (TDI) imaging. (2) Very high precision motion to support open-loop TDI observations. (3) A unique wind baffle/enclosure construction to maximize image quality and minimize construction costs. The telescope had first light in 1998 May and began regular survey operations in 2000.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: First measurement of baryon acoustic oscillations between redshift 0.8 and 2.2
abstract: AJR is grateful for support from the Ohio State University Center for Cosmology and ParticlePhysics. 
 
HGM acknowledges support from the Labex ILP (reference ANR-10-LABX-63) part of the Idex SUPER, and received financial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d'avenir under the reference ANR-11-IDEX-0004-02. 
 
GBZ is supported by NSFC Grant No. 11673025, and by a Royal Society Newton Advanced Fellowship. 
 
RT acknowledges support from the Science and Technology Facilities Council via an Ernest Rutherford Fellowship (grant number ST/K004719/1) 
 
CHC is grateful for support from Leibniz-Institut fur Astrophysik Potsdam (AIP). 
 
EB and PZ acknowledge support from the P2IO LabEx (ANR-10-LABX-0038). 
 
JLT acknowledges support from National Science Foundation grant AST-1615997. 
 
YW is supported by the NSFC grant number 11403034. 
 
WJP acknowledges support from the UK Space Agency through grant ST/K00283X/1, and WJP acknowledges support from the European Research Council through grant Darksurvey, and the UK Science & Technology Facilities Council through the consolidated grant ST/K0090X/1. 
 
ADM was partially supported by the NSF through grant numbers 1515404 and 1616168. 
 
IP acknowledges the support of the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the 'Investissements d'Avenir French government program managed by the AN. 
 
JPK acknowledges support from the ERC advanced grant LIDA. 
 
GR acknowledges support from the National Research Foundation of Korea (NRF) through NRF-SGER 2014055950 funded by the Korean Ministry of Education, Science and Technology (MoEST), and from the faculty research fund of Sejong University in 2016. 
 
Funding for SDSS-III and SDSS-IV has been provided by the Alfred P. Sloan Foundation and Participating Institutions. Additional funding for SDSS-III comes from the National Science Foundation and the U.S. Department of Energy Office of Science. Further information about both projects is available at www.sdss.org. SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions in both collaborations. In SDSS-III, these include the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. 
 
The Participating Institutions in SDSS-IV are Carnegie Mellon University, Colorado University, Boulder, Harvard-Smithsonian Center for Astrophysics Participation Group, Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe Max-Planck-Institut fuer Astrophysik (MPA Garching), Max-Planck-Institut fuer Extraterrestrische Physik (MPE), Max-Planck-Institut fuer Astronomie (MPIA Heidelberg), National Astronomical Observatories of China, New Mexico State University, New York University, The Ohio State University, Penn State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, University of Portsmouth, University of Utah, University of Wisconsin and Yale University. 
 
This work made use of the facilities and staff of the UK Sciama High Performance Computing cluster supported by the ICG, SEP-Net and the University of Portsmouth. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

title: Clustering of quasars in SDSS-IV eBOSS: study of potential systematics and bias determination
abstract: We study the first year of the eBOSS quasar sample in the redshift range 0.9 < z < 2.2 which includes 68,772 homogeneously selected quasars. We show that the main source of systematics in the evaluation of the correlation function arises from inhomogeneities in the quasar target selection, particularly related to the extinction and depth of the imaging data used for targeting. We propose a weighting scheme that mitigates these systematics. We measure the quasar correlation function and provide the most accurate measurement to date of the quasar bias in this redshift range, b(Q) = 2.45 +/- 0.05 at (z) over bar = 1.55, together with its evolution with redshift. We use this information to determine the minimum mass of the halo hosting the quasars and the characteristic halo mass, which we find to be both independent of redshift within statistical error. Using a recently-measured quasar-luminosity-function we also determine the quasar duty cycle. The size of this first year sample is insufficient to detect any luminosity dependence to quasar clustering and this issue should be further studied with the final similar to 500,000 eBOSS quasar sample.

title: Clustering of quasars in the first year of the SDSS-IV eBOSS survey : Interpretation and halo occupation distribution
abstract: SRT is grateful for support from the Campus de Excelencia Internacional UAM/CSIC. SRT, JC, FP acknowledge support from the Spanish MICINN Consolider-Ingenio 2010 Programme under grant MultiDark CSD2009-00064 MINECO Severo Ochoa Award SEV-2012-0249 and grant AYA2014-60641-C2-1-P. GY acknowledges financial support from MINECO/FEDER (Spain) under research grants AYA2012-31101 and AYA201563810-P.

title: The Sloan Digital Sky Survey Quasar Catalog: Twelfth data release
abstract: We present the Data Release 12 Quasar catalog (DR12Q) from the Baryon Oscillation Spectroscopic Survey (BOSS) of the Sloan Digital Sky Survey III. This catalog includes all SDSS-III/BOSS objects that were spectroscopically targeted as quasar candidates during the full survey and that are confirmed as quasars via visual inspection of the spectra, have luminosities M i [ z = 2] H 0 = 70 km s -1 Mpc -1 , Ω M = 0.3, and Ω Λ = 0.7), and either display at least one emission line with a full width at half maximum (FWHM) larger than 500 km s -1 or, if not, have interesting/complex absorption features. The catalog also includes previously known quasars (mostly from SDSS-I and II) that were reobserved by BOSS. The catalog contains 297 301 quasars (272 026 are new discoveries since the beginning of SDSS-III) detected over 9376 deg 2 with robust identification and redshift measured by a combination of principal component eigenspectra. The number of quasars with z > 2.15 (184 101, of which 167 742 are new discoveries) is about an order of magnitude greater than the number of z > 2.15 quasars known prior to BOSS. Redshifts and FWHMs are provided for the strongest emission lines (C iv, C iii], Mg ii). The catalog identifies 29 580 broad absorption line quasars and lists their characteristics. For each object, the catalog presents five-band ( u , g , r , i , z ) CCD-based photometry with typical accuracy of 0.03 mag together with some information on the optical morphology and the selection criteria. When available, the catalog also provides information on the optical variability of quasars using SDSS and Palomar Transient Factory multi-epoch photometry. The catalog also contains X-ray, ultraviolet, near-infrared, and radio emission properties of the quasars, when available, from other large-area surveys. The calibrated digital spectra, covering the wavelength region 3600–10 500 A at a spectral resolution in the range 1300 R < 2500, can be retrieved from the SDSS Catalog Archive Server. We also provide a supplemental list of an additional 4841 quasars that have been identified serendipitously outside of the superset defined to derive the main quasar catalog.

title: Ju n 20 00 The Sloan Digital Sky Survey : Technical Summary
abstract: The Sloan Digital Sky Survey (SDSS) will provide the data to support detailed investigations of the distribution of luminous and non-luminous matter in the Universe: a photometrically and astrometrically calibrated digital imaging survey of π steradians above about Galactic latitude 30 in five broad optical bands to a depth of g ∼ 23, and a spectroscopic survey of the approximately 10 brightest galaxies and 10 brightest quasars found in the photometric object catalog produced by the imaging survey. This paper summarizes the observational parameters and data products of the SDSS, and serves as an introduction to extensive technical on-line documentation.

title: The Seventh Data Release of the Sloan Digital Sky Survey
abstract: This paper describes the Seventh Data Release of the Sloan Digital Sky Survey (SDSS), marking the completion of the original goals of the SDSS and the end of the phase known as SDSS-II. It includes 11,663 deg^2 of imaging data, with most of the ~2000 deg^2 increment over the previous data release lying in regions of low Galactic latitude. The catalog contains five-band photometry for 357 million distinct objects. The survey also includes repeat photometry on a 120° long, 2°.5 wide stripe along the celestial equator in the Southern Galactic Cap, with some regions covered by as many as 90 individual imaging runs. We include a co-addition of the best of these data, going roughly 2 mag fainter than the main survey over 250 deg^2. The survey has completed spectroscopy over 9380 deg^2; the spectroscopy is now complete over a large contiguous area of the Northern Galactic Cap, closing the gap that was present in previous data releases. There are over 1.6 million spectra in total, including 930,000 galaxies, 120,000 quasars, and 460,000 stars. The data release includes improved stellar photometry at low Galactic latitude. The astrometry has all been recalibrated with the second version of the USNO CCD Astrograph Catalog, reducing the rms statistical errors at the bright end to 45 milliarcseconds per coordinate. We further quantify a systematic error in bright galaxy photometry due to poor sky determination; this problem is less severe than previously reported for the majority of galaxies. Finally, we describe a series of improvements to the spectroscopic reductions, including better flat fielding and improved wavelength calibration at the blue end, better processing of objects with extremely strong narrow emission lines, and an improved determination of stellar metallicities.

title: SDSS-III: MASSIVE SPECTROSCOPIC SURVEYS OF THE DISTANT UNIVERSE, THE MILKY WAY, AND EXTRA-SOLAR PLANETARY SYSTEMS
abstract: Building on the legacy of the Sloan Digital Sky Survey (SDSS-I and II), SDSS-III is a program of four spectroscopic surveys on three scientific themes: dark energy and cosmological parameters, the history and structure of the Milky Way, and the population of giant planets around other stars. In keeping with SDSS tradition, SDSS-III will provide regular public releases of all its data, beginning with SDSS DR8 (which occurred in Jan 2011). This paper presents an overview of the four SDSS-III surveys. BOSS will measure redshifts of 1.5 million massive galaxies and Lya forest spectra of 150,000 quasars, using the BAO feature of large scale structure to obtain percent-level determinations of the distance scale and Hubble expansion rate at z 100 per resolution element), H-band (1.51-1.70 micron) spectra of 10^5 evolved, late-type stars, measuring separate abundances for ~15 elements per star and creating the first high-precision spectroscopic survey of all Galactic stellar populations (bulge, bar, disks, halo) with a uniform set of stellar tracers and spectral diagnostics. MARVELS will monitor radial velocities of more than 8000 FGK stars with the sensitivity and cadence (10-40 m/s, ~24 visits per star) needed to detect giant planets with periods up to two years, providing an unprecedented data set for understanding the formation and dynamical evolution of giant planet systems.

title: THE BARYON OSCILLATION SPECTROSCOPIC SURVEY OF SDSS-III
abstract: The Baryon Oscillation Spectroscopic Survey (BOSS) is designed to measure the scale of baryon acoustic oscillations (BAO) in the clustering of matter over a larger volume than the combined efforts of all previous spectroscopic surveys of large-scale structure. BOSS uses 1.5 million luminous galaxies as faint as i = 19.9 over 10,000 deg2 to measure BAO to redshifts z < 0.7. Observations of neutral hydrogen in the Lyα forest in more than 150,000 quasar spectra (g < 22) will constrain BAO over the redshift range 2.15 < z < 3.5. Early results from BOSS include the first detection of the large-scale three-dimensional clustering of the Lyα forest and a strong detection from the Data Release 9 data set of the BAO in the clustering of massive galaxies at an effective redshift z = 0.57. We project that BOSS will yield measurements of the angular diameter distance dA to an accuracy of 1.0% at redshifts z = 0.3 and z = 0.57 and measurements of H(z) to 1.8% and 1.7% at the same redshifts. Forecasts for Lyα forest constraints predict a measurement of an overall dilation factor that scales the highly degenerate DA (z) and H –1(z) parameters to an accuracy of 1.9% at z ~ 2.5 when the survey is complete. Here, we provide an overview of the selection of spectroscopic targets, planning of observations, and analysis of data and data quality of BOSS.

title: The Eighth Data Release of the Sloan Digital Sky Survey: First Data from SDSS-III
abstract: The Sloan Digital Sky Survey (SDSS) started a new phase in 2008 August, with new instrumentation and new surveys focused on Galactic structure and chemical evolution, measurements of the baryon oscillation feature in the clustering of galaxies and the quasar Lyα forest, and a radial velocity search for planets around ~8000 stars. This paper describes the first data release of SDSS-III (and the eighth counting from the beginning of the SDSS). The release includes five-band imaging of roughly 5200 deg2 in the southern Galactic cap, bringing the total footprint of the SDSS imaging to 14,555 deg2, or over a third of the Celestial Sphere. All the imaging data have been reprocessed with an improved sky-subtraction algorithm and a final, self-consistent photometric recalibration and flat-field determination. This release also includes all data from the second phase of the Sloan Extension for Galactic Understanding and Exploration (SEGUE-2), consisting of spectroscopy of approximately 118,000 stars at both high and low Galactic latitudes. All the more than half a million stellar spectra obtained with the SDSS spectrograph have been reprocessed through an improved stellar parameter pipeline, which has better determination of metallicity for high-metallicity stars.

title: THE WIDE-FIELD INFRARED SURVEY EXPLORER (WISE): MISSION DESCRIPTION AND INITIAL ON-ORBIT PERFORMANCE
abstract: The all sky surveys done by the Palomar Observatory Schmidt, the European Southern Observatory Schmidt, and 
the United Kingdom Schmidt, the InfraRed Astronomical Satellite, and the Two Micron All Sky Survey have 
proven to be extremely useful tools for astronomy with value that lasts for decades. The Wide-field Infrared 
Survey Explorer (WISE) is mapping the whole sky following its launch on 2009 December 14. WISE began 
surveying the sky on 2010 January 14 and completed its first full coverage of the sky on July 17. The survey 
will continue to cover the sky a second time until the cryogen is exhausted (anticipated in 2010 November). 
WISE is achieving 5σ point source sensitivities better than 0.08, 0.11, 1, and 6 mJy in unconfused regions on 
the ecliptic in bands centered at wavelengths of 3.4, 4.6, 12, and 22μm. Sensitivity improves toward the ecliptic 
poles due to denser coverage and lower zodiacal background. The angular resolution is 6".1, 6".4, 6".5, and 12".0 at 3.4, 4.6, 12, and 22μm, and the astrometric precision for high signal-to-noise sources is better than 0".15.

title: The Sdss-Iv Extended Baryon Oscillation Spectroscopic Survey: Quasar Target Selection
abstract: As part of the Sloan Digital Sky Survey (SDSS) IV the extended Baryon Oscillation Spectroscopic Survey (eBOSS) will improve measurements of the cosmological distance scale by applying the Baryon Acoustic Oscillation (BAO) method to quasar samples. eBOSS will adopt two approaches to target quasars over 7500 deg^2. First, a "CORE" quasar sample will combine the optical selection in ugriz using a likelihood-based routine called XDQSOz, with a mid-IR-optical color cut. eBOSS CORE selection (to g 2.1 quasars. Second, a selection based on variability in multi-epoch imaging from the Palomar Transient Factory should recover an additional ~3–4 deg^(−2)z > 2.1 quasars to g 2.1 will be used to improve BAO measurements in the Lyα Forest. Beyond its key cosmological goals, eBOSS should be the next-generation quasar survey, comprising >500,000 new quasars and >500,000 uniformly selected spectroscopically confirmed 0.9 < z < 2.2 quasars. At the conclusion of eBOSS, the SDSS will have provided unique spectra for more than 800,000 quasars.

title: THE SDSS-III BARYON OSCILLATION SPECTROSCOPIC SURVEY: QUASAR TARGET SELECTION FOR DATA RELEASE NINE
abstract: The SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), a five-year spectroscopic survey of 10,000 deg2, achieved first light in late 2009. One of the key goals of BOSS is to measure the signature of baryon acoustic oscillations (BAOs) in the distribution of Lyα absorption from the spectra of a sample of ~150,000 z > 2.2 quasars. Along with measuring the angular diameter distance at z ≈ 2.5, BOSS will provide the first direct measurement of the expansion rate of the universe at z > 2. One of the biggest challenges in achieving this goal is an efficient target selection algorithm for quasars in the redshift range 2.2 2.20 quasars deg-2). This "CORE" subsample will be fixed for Years Two through Five of the survey. For the remaining 20 targets deg-2, we will continue to develop improved selection techniques, including the use of additional data sets beyond the Sloan Digital Sky Survey (SDSS) imaging data. In this paper, we describe the evolution and implementation of the BOSS QTS algorithms during the first two years of BOSS operations (through 2011 July), in support of the science investigations based on these data, and we analyze the spectra obtained during the first year. During this year, 11,263 new z > 2.20 quasars were spectroscopically confirmed by BOSS, roughly double the number of previously known quasars with z > 2.20. Our current algorithms select an average of 15 z > 2.20 quasars deg-2 from 40 targets deg-2 using single-epoch SDSS imaging. Multi-epoch optical data and data at other wavelengths can further improve the efficiency and completeness of BOSS QTS.

title: The Sloan Digital Sky Survey Reverberation Mapping Project: Velocity Shifts of Quasar Emission Lines
abstract: Quasar emission lines are often shifted from the systemic velocity due to various dynamical and radiative processes in the line-emitting region. The level of these velocity shifts depends both on the line species and on quasar properties. We study velocity shifts for the line peaks of various narrow and broad quasar emission lines relative to systemic using a sample of 849 quasars from the Sloan Digital Sky Survey Reverberation Mapping (SDSS-RM) project. The coadded (from 32 epochs) spectra of individual quasars have sufficient signal-to-noise ratio (SNR) to measure stellar absorption lines to provide reliable systemic velocity estimates, as well as weak narrow emission lines. The sample also covers a large dynamic range in quasar luminosity (~2 dex), allowing us to explore potential luminosity dependence of the velocity shifts. We derive average line peak velocity shifts as a function of quasar luminosity for different lines, and quantify their intrinsic scatter. We further quantify how well the peak velocity can be measured for various lines as a function of continuum SNR, and demonstrate there is no systematic bias in the line peak measurements when the spectral quality is degraded to as low as SNR~3 per SDSS pixel. Based on the observed line shifts, we provide empirical guidelines on redshift estimation from [OII]3728, [OIII]5008, [NeV]3426, MgII, CIII], HeII1640, broad Hbeta, CIV, and SiIV, which are calibrated to provide unbiased systemic redshifts in the mean, but with increasing intrinsic uncertainties of 46, 56, 119, 205, 233, 242, 400, 415, and 477 km/s, in addition to the measurement uncertainties. These more realistic redshift uncertainties are generally much larger than the formal uncertainties reported by the redshift pipelines for spectroscopic quasar surveys, and demonstrate the infeasibility of measuring quasar redshifts to better than ~200 km/s with only broad lines.

title: The clustering of galaxies in the sdss-iii baryon oscillation spectroscopic survey: Baryon acoustic oscillations in the data release 9 spectroscopic galaxy sample
abstract: We present a one per cent measurement of the cosmic distance scale from the detections of the baryon acoustic oscillations in the clustering of galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS), which is part of the Sloan Digital Sky Survey III (SDSS-III). Our results come from the Data Release 11 (DR11) sample, containing nearly one million galaxies and covering approximately $8\,500$ 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 $\Lambda$CDM cosmological model, the DR11 sample covers a volume of 13\,Gpc${}^3$ 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 baryon acoustic oscillation (BAO) feature. The acoustic features are detected at a significance of over $7\,\sigma$ 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, $r_d$, which has a value of $r_{d,{\rm fid}}=149.28\,$Mpc in our fiducial cosmology. We find $D_V=(1264\pm25\,{\rm Mpc})(r_d/r_{d,{\rm fid}})$ at $z=0.32$ and $D_V=(2056\pm20\,{\rm Mpc})(r_d/r_{d,{\rm fid}})$ 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 $D_A=(1421\pm20\,{\rm Mpc})(r_d/r_{d,{\rm fid}})$ and $H=(96.8\pm3.4\,{\rm km/s/Mpc})(r_{d,{\rm fid}}/r_d)$. 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 cold dark matter model with a cosmological constant.

title: A 2 . 5 % measurement of the growth rate from small-scale redshift space clustering of SDSS-III CMASS galaxies
abstract: We perform the first fit to the anisotropic clustering of SDSS-III CMASS DR10 galaxies on scales of ∼ 0.8−32 h−1 Mpc. A standard halo occupation distribution model evaluated near the best fit Planck 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 halos of fσ8(z = 0.57) = 0.450 ± 0.011. Since this constraint includes both quasi-linear and nonlinear 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 fit Planck cosmology, we also find that 10% of CMASS galaxies are satellites in halos 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 modeling uncertainties and degeneracies with cosmological parameters.

title: The Effect of Fiber Collisions on the Galaxy Power Spectrum Multipole
abstract: Fiber-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 catalogs, we demonstrate that fiber collisions have a significant impact on the power spectrum, $P(k)$, monopole and quadrupole that exceeds sample variance at scales smaller than $k\sim0.1~h/Mpc$. 
We present two methods to account for fiber collisions in the power spectrum. The first, statistically reconstructs the clustering of fiber collided galaxy pairs by modeling the distribution of the line-of-sight displacements between them. It also properly accounts for fiber 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 catalogs with residuals of $<0.5\%$ at $k=0.3~h/Mpc$ and $<4\%$ at $k=0.83~h/Mpc$ -- a significant improvement over existing correction methods. The quadrupole, however, does not improve significantly. 
The second method models the effect of fiber collisions on the power spectrum as a convolution with a configuration space top-hat function that depends on the physical scale of fiber collisions. It directly computes theoretical predictions of the fiber-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 fiber 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 analyze galaxy power spectrum multipole measurements to much smaller scales than previously possible.

title: SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 12: galaxy target selection and large-scale structure catalogues
abstract: The Baryon Oscillation Spectroscopic Survey (BOSS), part of the Sloan Digital Sky Survey (SDSS) III project, has provided the largest survey of galaxy redshifts available to date, in terms of both the number of galaxy redshifts measured by a single survey, and the effective cosmological volume covered. Key to analysing the clustering of these data to provide cosmological measurements is understanding the detailed properties of this sample. Potential issues include variations in the target catalogue caused by changes either in the targeting algorithm or properties of the data used, the pattern of spectroscopic observations, the spatial distribution of targets for which redshifts were not obtained, and variations in the target sky density due to observational systematics. We document here the target selection algorithms used to create the galaxy samples that comprise BOSS. We also present the algorithms used to create large-scale structure catalogues for the final Data Release (DR12) samples and the associated random catalogues that quantify the survey mask. The algorithms are an evolution of those used by the BOSS team to construct catalogues from earlier data, and have been designed to accurately quantify the galaxy sample. The code used, designated MKSAMPLE, is released with this paper.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: structure growth rate measurement from the anisotropic quasar power spectrum in the redshift range $0.8 < z < 2.2$
abstract: Author(s): Gil-Marin, H; Guy, J; Zarrouk, P; Burtin, E; Chuang, CH; Percival, WJ; Ross, AJ; Ruggeri, R; Tojerio, R; Zhao, GB; Wang, Y; Bautista,  Hou, J; Sanchez, AG; Pâris, I; Baumgarten, F; Brownstein, JR; Dawson, KS; Eftekharzadeh, S; Gonzalez-Perez, V; Habib, S; Heitmann, K; Myers, AD; Rossi, G; Schneider, DP; Seo, HJ; Tinker, JL; Zhao, C |  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.

title: EZmocks: Extending the Zel'dovich approximation to generate mock galaxy catalogues with accurate clustering statistics
abstract: This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society

title: The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release
abstract: We reproduce the galaxy clustering catalogue from the SDSS-III Baryon Oscillation Spectroscopic Survey Final Data Release (BOSS DR11&DR12) with high fidelity on all relevant scales in order to allow a robust analysis of baryon acoustic oscillations and redshift space distortions. We have generated (6000) 12 288 MultiDark PATCHY BOSS (DR11) DR12 light cones corresponding to an effective volume of similar to 192 000 [h(-1) Gpc](3) (the largest ever simulated volume), including cosmic evolution in the redshift range from 0.15 to 0.75. The mocks have been calibrated using a reference galaxy catalogue based on the halo abundance matching modelling of the BOSS DR11&DR12 galaxy clustering data and on the data themselves. The production follows three steps. First, we apply the PATCHY code to generate a dark matter field and an object distribution including non-linear stochastic galaxy bias. Secondly, we run the halo/stellar distribution reconstruction HADRON code to assign masses to the various objects. This step uses the mass distribution as a function of local density and non-local indicators (i.e. tidal field tensor eigenvalues and relative halo exclusion separation for massive objects) from the reference simulation applied to the corresponding patchy dark matter and galaxy distribution. Finally, we apply the SUGAR code to build the light cones. The resulting MultiDarkPATCHY mock light cones reproduce the number density, selection function, survey geometry, and in general within 1 sigma, for arbitrary stellar mass bins, the power spectrum up to k = 0.3 h Mpc(-1), the two-point correlation functions down to a few Mpc scales, and the three-point statistics of the BOSS DR11&DR12 galaxy samples.

title: Embedding realistic surveys in simulations through volume remapping
abstract: Connecting cosmological simulations to real-world observational programs is often complicated by a mismatch in geometry: while surveys often cover highly irregular cosmological volumes, simulations are customarily performed in a periodic cube. We describe a technique to remap this cube into elongated box-like shapes that are more useful for many applications. The remappings are one-to-one, volume-preserving, keep local structures intact, and involve minimal computational overhead.

title: Planck 2018 results
abstract: Author(s): Aghanim, N; Akrami, Y; Ashdown, M;  Ballardini, M; Banday, AJ; Barreiro, RB; Bartolo, N; Basak, S; Battye, R; Benabed, K; Bernard, JP; Bersanelli, M; Bielewicz, P; Bock, JJ; Bond, JR; Borrill, J; Bouchet, FR; Boulanger, F; Bucher, M; Burigana, C; Butler, RC; Calabrese, E; Cardoso, JF; Carron, J; Challinor, A; Chiang, HC; Chluba, J; Colombo, LPL; Combet, C; Contreras, D; Crill, BP; Cuttaia, F; De Bernardis, P; De Zotti, G; Delabrouille, J; Delouis, JM; Di Valentino, E; Diego, JM; Dore, O; Douspis, M; Ducout, A; Dupac, X; Dusini, S; Efstathiou, G; Elsner, F; Enslin, TA; Eriksen, HK; Fantaye, Y; Farhang, M; Fergusson, J; Fernandez-Cobos, R; Finelli, F; Forastieri, F; Frailis, M; Fraisse, AA; Franceschi, E; Frolov, A; Galeotta, S; Galli, S; Ganga, K; Genova-Santos, RT; Gerbino, M; Ghosh, T; Gonzalez-Nuevo, J; Gorski, KM; Gratton, S; Gruppuso, A; Gudmundsson, JE; Hamann, J; Handley, W; Hansen, FK; Herranz, D; Hildebrandt, SR; Hivon, E; Huang, Z; Jaffe, AH; Jones, WC; Karakci, A; Keihanen, E; Keskitalo, R; Kiiveri, K; Kim, J; Kisner, TS | Abstract:  We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters. Improved modelling of the small-scale polarization leads to more robust constraints on many parameters, with residual modelling uncertainties estimated to affect them only at the 0.5σ level. We find good consistency with the standard spatially-flat 6-parameter ΛCDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base ΛCDM"in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density ωch2 = 0.120 ± 0.001, baryon density ωbh2 = 0.0224 ± 0.0001, scalar spectral index ns = 0.965 ± 0.004, and optical depth τ = 0.054 ± 0.007 (in this abstract we quote 68% confidence regions on measured parameters and 95% on upper limits). The angular acoustic scale is measured to 0.03% precision, with 100θ∗ = 1.0411 ± 0.0003. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-ΛCDM cosmology, the inferred (model-dependent) late-Universe parameters are: Hubble constant H0 = (67.4 ± 0.5) km s-1 Mpc-1; matter density parameter ωm = 0.315 ± 0.007; and matter fluctuation amplitude σ8 = 0.811 ± 0.006. We find no compelling evidence for extensions to the base-ΛCDM model. Combining with baryon acoustic oscillation (BAO) measurements (and considering single-parameter extensions) we constrain the effective extra relativistic degrees of freedom to be Neff = 2.99 ± 0.17, in agreement with the Standard Model prediction Neff = 3.046, and find that the neutrino mass is tightly constrained to mν l 0.12 eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base ΛCDM at over 2σ, which pulls some parameters that affect the lensing amplitude away from the ΛCDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. The joint constraint with BAO measurements on spatial curvature is consistent with a flat universe, ωK = 0.001 ± 0.002. Also combining with Type Ia supernovae (SNe), the dark-energy equation of state parameter is measured to be w0 = -1.03 ± 0.03, consistent with a cosmological constant. We find no evidence for deviations from a purely power-law primordial spectrum, and combining with data from BAO, BICEP2, and Keck Array data, we place a limit on the tensor-to-scalar ratio r0.002 l 0.06. Standard big-bang nucleosynthesis predictions for the helium and deuterium abundances for the base-ΛCDM cosmology are in excellent agreement with observations. The Planck base-ΛCDM results are in good agreement with BAO, SNe, and some galaxy lensing observations, but in slight tension with the Dark Energy Survey's combined-probe results including galaxy clustering (which prefers lower fluctuation amplitudes or matter density parameters), and in significant, 3.6σ, tension with local measurements of the Hubble constant (which prefer a higher value). Simple model extensions that can partially resolve these tensions are not favoured by the Planck data.

title: The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: Testing gravity with redshift-space distortions using the power spectrum multipoles
abstract: 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 deg^2. 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 D_V(z_eff)/r_s(z_d) = 13.89 ± 0.18, the Alcock–Paczynski parameter F_AP(z_eff) = 0.679 ± 0.031 and the growth rate of structure f (z_eff)σ_8(z_eff) = 0.419 ± 0.044 at the effective redshift z_eff = 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 fσ_8 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 D_V/r_s or F_AP. 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 σ_8 between CMASS and Planck.

title: The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: anisotropic galaxy clustering in Fourier space
abstract: We investigate the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 sample, which consists of 1198 006 galaxies in the redshift range 0.2 < z < 0.75 and a sky coverage of 10 252 deg(2). We analyse this data set in Fourier space, using the power-spectrum multipoles to measure redshift-space distortions simultaneously with the Alcock-Paczynski effect and the baryon acoustic oscillation scale. We include the power-spectrum monopole, quadrupole and hexadecapole in our analysis and compare our measurements with a perturbation-theory-based model, while properly accounting for the survey window function. To evaluate the reliability of our analysis pipeline, we participate in a mock challenge, which results in systematic uncertainties significantly smaller than the statistical uncertainties. While the high-redshift constraint on f sigma(8) at z(eff) = 0.61 indicates a small (similar to 1.4 sigma) deviation from the prediction of the Planck Lambda CDM (Lambda cold dark matter) model, the low-redshift constraint is in good agreement with Planck Lambda CDM. 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.

title: The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey : cosmological implications of the Fourier space wedges of the final sample
abstract: 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 Lambda cold dark matter (Lambda CDM) cosmology, we constrain the matter density to Omega M = 0.311(-0.010)(+ 0.009) and the Hubble parameter to H-0 = 67.6(-0.6)(+0.7) km s(-1) Mpc(-1), 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 Lambda CDM paradigm. For example, we constrain the equation-of-state parameter to omega =-1.019(-0.039)(+0.048) . 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.

title: Computer simulation using particles
abstract: Computer experiments using particle models A one-dimensional plasma model The simulation program Time integration schemes The particle-mesh force calculation The solution of field equations Collisionless particle models Particle-particle/particle-mesh algorithms Plasma simulation Semiconductor device simulation Astrophysics Solids, liquids and phase changes Fourier transforms Fourier series and finite Fourier transforms Bibliography Index

title: Accurate estimators of correlation functions in Fourier space
abstract: Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a sum over images, each of them corresponding to the Fourier content displaced by increasing multiples of the sampling frequency of the grid. These spurious contributions limit the accuracy in the estimation of Fourier-space statistics, and are typically ameliorated by simultaneously increasing grid size and discarding high-frequency modes. This results in inefficient estimates for e.g. the power spectrum when desired systematic biases are well under per-cent level. We show that using interlaced grids removes odd images, which include the dominant contribution to aliasing. In addition, we discuss the choice of interpolation kernel used to define density perturbations on the FFT grid and demonstrate that using higher-order interpolation kernels than the standard Cloud in Cell algorithm results in significant reduction of the remaining images. We show that combining fourth-order interpolation with interlacing gives very accurate Fourier amplitudes and phases of density perturbations. This results in power spectrum and bispectrum estimates that have systematic biases below 0.01% all the way to the Nyquist frequency of the grid, thus maximizing the use of unbiased Fourier coefficients for a given grid size and greatly reducing systematics for applications to large cosmological datasets.

title: The Cosmic Linear Anisotropy Solving System (CLASS). Part II: Approximation schemes
abstract: Boltzmann codes are used extensively by several groups for constraining cosmo- logical parameters with Cosmic Microwave Background and Large Scale Structure data. This activity is computationally expensive, since a typical project requires from 10 4 to 10 5 Boltz- mann code executions. The newly released code CLASS (Cosmic Linear Anisotropy Solving System) incorporates improved approximation schemes leading to a simultaneous gain in speed and precision. We describe here the three approximations used by CLASS for basic �CDM models, namely: a baryon-photon tight-coupling approximation which can be set to first order, second order or to a compromise between the two; an ultra-relativistic fluid approximation which had not been implemented in public distributions before; and finally a radiation streaming approximation taking reionisation into account.

title: The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the LOS-dependent power spectrum of DR12 BOSS galaxies
abstract: HGM is grateful for support from the UK Science and Technology Facilities Council through the grant ST/I001204/1. WJP is grateful for support from the UK Science and Technology Facilities Research Council through the grant ST/I001204/1, and the European Research Council through the grant “Darksurvey”, reference 614030. FSK acknowledges the support of the Karl-Schwarzschild Program from the Leibniz Society.

title: Rapid modelling of the redshift-space power spectrum multipoles for a masked density field
abstract: In this work we reformulate the forward modelling of the redshift-space power spectrum multipole moments for a masked density field, as encountered in galaxy redshift surveys. Exploiting the symmetries of the redshift-space correlation function, we provide a masked-field generalisation of the Hankel transform relation between the multipole moments in real and Fourier space. Using this result, we detail how a likelihood analysis requiring computation for a broad range of desired $P(k)$ models may be executed $10^3-10^4$ times faster than with other common approaches, together with significant gains in spectral resolution. We present a concrete application to the complex angular geometry of the VIPERS PDR-1 release and discuss the validity of this technique for finite-angle surveys.

title: Beyond the plane-parallel approximation for redshift surveys
abstract: Author(s): Castorina, E; White, M |  Redshift -space distortions privilege the location of the observer in cosmological redshift surveys, breaking the translational symmetry of the underlying theory. This violation of statistical homogeneity has consequences for the modelling of clustering observables, leading to what are frequently called 'wide-angle effects'.We study these effects analytically, computing their signature in the clustering of the multipoles in configuration and Fourier space. We take into account both physical wide-angle contributions as well as the terms generated by the galaxy selection function. Similar considerations also affect the way power spectrum estimators are constructed. We quantify in an analytical way the biases that enter and clarify the relation between what we measure and the underlying theoretical modelling. The presence of an angular window function is also discussed. Motivated by this analysis, we present new estimators for the three dimensional Cartesian power spectrum and bispectrum multipoles written in terms of spherical Fourier-Bessel coefficients.We show how the latter have several interesting properties, allowing in particular a clear separation between angular and radial modes.

title: The zeldovich approximation and wide-angle redshift-space distortions
abstract: Author(s): Castorina, E; White, M |  The contribution of line-of-sight (LOS) peculiar velocities to the observed redshift of objects breaks the translational symmetry of the underlying theory, modifying the predicted two-point functions. These 'wide-angle effects' have mostly been studied using linear perturbation theory in the context of the multipoles of the correlation function and power spectrum. In this work, we present the first calculation of wide-angle terms in the Zeldovich approximation, which is known to be more accurate than linear theory on scales probed by the next generation of galaxy surveys.We present the exact result for dark matter and perturbatively biased tracers as well as the small angle expansion of the configuration- and Fourier-space two-point functions and the connection to the multifrequency angular power spectrum. We compare different definitions of the LOS direction and discuss how to translate between them. We show that wide-angle terms can reach tens of percent of the total signal in a measurement at low redshift in some approximations, and that a generic feature of wide-angle effects is to slightly shift the Baryon Acoustic Oscillation scale.

title: The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights
abstract: 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 fσ_8 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.

title: An evolution free test for non-zero cosmological constant
abstract: The cosmological constant has recently been questioned because of difficulties in fitting the standard Λ=0 cosmological models to observational data1,2. We propose here a cosmological test that is a sensitive estimator of Λ. This test is unusual in that it involves no correction for evolutionary effects. We present here the idealised conception of the method, and hint at the statistical problem that its realisation entails.

title: Planck 2018 results. I. Overview and the cosmological legacy of Planck
abstract: The European Space Agency's Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter LCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (theta_*) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the LCDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances.

title: Why your model parameter confidences might be too optimistic - unbiased estimation of the inverse covariance matrix
abstract: The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent analysis, focusing on estimators of the inverse covariance matrix. Furthermore, we study under which circumstances the estimated covariance matrix is invertible.  We perform Monte-Carlo simulations to investigate the behaviour of estimators for the inverse covariance matrix, depending on the number of independent data sets and the number of variables of the data vectors.  We find that the inverse of the maximum-likelihood estimator of the covariance is biased, the amount of bias depending on the ratio of the number of bins (data vector variables), p , to the number of data sets, n . This bias inevitably leads to an – in extreme cases catastrophic – underestimation of the size of confidence regions. We report on a method to remove this bias for the idealised case of Gaussian noise and statistically independent data vectors. Moreover, we demonstrate that marginalisation over parameters introduces a bias into the marginalised log-likelihood function. Measures of the sizes of confidence regions suffer from the same problem. Furthermore, we give an analytic proof for the fact that the estimated covariance matrix is singular if $p>n$.

title: The clustering of Galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: including covariance matrix errors
abstract: We present improved methodology for including covariance matrices in the error budget of Baryon Oscillation Spectroscopic Survey (BOSS) galaxy clustering measurements, revisiting Data Release 9 (DR9) analyses, and describing a method that is used in DR10/11 analyses presented in companion papers. The precise analysis method adopted is becoming increasingly important, due to the precision that BOSS can now reach: even using as many as 600 mock catalogues to estimate covariance of two-point clustering measurements can still lead to an increase in the errors of ∼20 per cent, depending on how the cosmological parameters of interest are measured. In this paper, we extend previous work on this contribution to the error budget, deriving formulae for errors measured by integrating over the likelihood, and to the distribution of recovered best-fitting parameters fitting the simulations also used to estimate the covariance matrix. Both are situations that previous analyses of BOSS have considered. We apply the formulae derived to baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) measurements from BOSS in our companion papers. To further aid these analyses, we consider the optimum number of bins to use for two-point measurements using the monopole power spectrum or correlation function for BAO, and the monopole and quadrupole moments of the correlation function for anisotropic-BAO and RSD measurements.

title: A Limited Memory Algorithm for Bound Constrained Optimization
abstract: An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function. It is shown how to take advantage of the form of the limited memory approximation to implement the algorithm efficiently. The results of numerical tests on a set of large problems are reported.

title: emcee: The MCMC Hammer
abstract: We introduce a stable, well tested Python implementation of the affine-invariant ensemble sampler for Markov chain Monte Carlo (MCMC) proposed by Goodman & Weare (2010). The code is open source and has already been used in several published projects in the astrophysics literature. The algorithm behind emcee has several advantages over traditional MCMC sampling methods and it has excellent performance as measured by the autocorrelation time (or function calls per independent sample). One major advantage of the algorithm is that it requires hand-tuning of only 1 or 2 parameters compared to ~N2 for a traditional algorithm in an N-dimensional parameter space. In this document, we describe the algorithm and the details of our implementation. Exploiting the parallelism of the ensemble method, emcee permits any user to take advantage of multiple CPU cores without extra effort. The code is available online at http://dan.iel.fm/emcee under the GNU General Public License v2.

title: The Time evolution of bias
abstract: We study the evolution of the bias factor b and the mass-galaxy correlation coefficient r in a simple analytic model for galaxy formation and the gravitational growth of clustering. The model shows that b and r can be strongly time dependent but tend to approach unity even if galaxy formation never ends as the gravitational growth of clustering debiases the older galaxies. The presence of random fluctuations in the sites of galaxy formation relative to the mass distribution can cause large and rapidly falling bias values at high redshift.