SDSS-IV Extended Baryon Oscillation Spectroscopic Research Articles

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the growth rate of structure from the small-scale clustering of the luminous red galaxy sample

ABSTRACT We measure the small-scale clustering of the Data Release 16 extended Baryon Oscillation Spectroscopic Survey Luminous Red Galaxy sample, corrected for fibre-collisions using Pairwise Inverse Probability weights, which give unbiased clustering measurements on all scales. We fit to the monopole and quadrupole moments and to the projected correlation function over the separation range $7-60\, h^{-1}{\rm Mpc}$ with a model based on the aemulus cosmological emulator to measure the growth rate of cosmic structure, parametrized by fσ8. We obtain a measurement of fσ8(z = 0.737) = 0.408 ± 0.038, which is 1.4σ lower than the value expected from 2018 Planck data for a flat ΛCDM model, and is more consistent with recent weak-lensing measurements. The level of precision achieved is 1.7 times better than more standard measurements made using only the large-scale modes of the same sample. We also fit to the data using the full range of scales $0.1\text{--}60\, h^{-1}{\rm Mpc}$ modelled by the aemulus cosmological emulator and find a 4.5σ tension in the amplitude of the halo velocity field with the Planck + ΛCDM model, driven by a mismatch on the non-linear scales. This may not be cosmological in origin, and could be due to a breakdown in the Halo Occupation Distribution model used in the emulator. Finally, we perform a robust analysis of possible sources of systematics, including the effects of redshift uncertainty and incompleteness due to target selection that were not included in previous analyses fitting to clustering measurements on small scales.

Primordial non-Gaussianity from the completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey II: measurements in Fourier space with optimal weights

ABSTRACTWe present measurements of the local primordial non-Gaussianity parameter $f_{\mathrm{NL}}^\mathrm{local} $from the clustering of 343 708 quasars with redshifts 0.8 < z < 2.2 distributed over 4808 deg2 from the final data release (DR16) of the extended Baryon Acoustic Oscillation Spectroscopic Survey (eBOSS), the largest volume spectroscopic survey up to date. Our analysis is performed in Fourier space, using the power spectrum monopole at very large scales to constrain the scale-dependent halo bias. We demonstrate the robustness of our analysis pipeline with EZ-mock catalogues that simulate the eBOSS DR16 target selection. We carefully assess the impact of systematics on our measurement, exploiting a novel neural network scheme for cleaning the DR16 sample as well as test multiple contamination removal methods. We estimate the bias due to the overcorrection of the systematic removal to be sub-dominant compared to the statistical uncertainty. We find fNL = −12 ± 21 (68 per cent confidence) for the main clustering sample including quasars with redshifts between 0.8 and 2.2, after applying redshift weighting techniques, designed for non-Gaussianity measurement from large scales structure, to optimize our analysis, which improve our results by 37 per cent.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: cosmological implications from multitracer BAO analysis with galaxies and voids

ABSTRACT We construct cosmic void catalogues with the dive void finder upon SDSS BOSS DR12 and eBOSS DR16 galaxy samples with BAO reconstruction, and perform a joint BAO analysis using different types of galaxies and the corresponding voids. The BAO peak is evident for the galaxy–galaxy, galaxy–void, and void–void correlation functions of all data sets, including the ones cross-correlating LRG and ELG samples. Two multitracer BAO fitting schemes are tested, one combining the galaxy and void correlation functions with a weight applied to voids, and the other using a single BAO dilation parameter for all clustering measurements. Both methods produce consistent results with mock catalogues, and on average ∼10 per cent improvements of the BAO statistical uncertainties are observed for all samples, compared to the results from galaxies alone. By combining the clustering of galaxies and voids, the uncertainties of BAO measurements from the SDSS data are reduced by 5–15 per cent, yielding 0.9 per cent, 0.8 per cent, 1.1 per cent, 2.3 per cent, and 2.9 per cent constraints on the distance $D_{_{\rm V}}(z)$, at effective redshifts 0.38, 0.51, 0.70, 0.77, and 0.85, respectively. When combined with BAO measurements from SDSS MGS, QSO, and Lyα samples, as well as the BBN results, we obtain $H_0 = 67.58 \pm 0.91\, {\rm km}\, {\rm s}^{-1}\, {\rm Mpc}^{-1}$, Ωm = 0.290 ± 0.015, and $\Omega _\Lambda h^2 = 0.3241 \pm 0.0079$ in the flat-ΛCDM framework, where the 1σ uncertainties are around 6 per cent, 6 per cent, and 17 per cent smaller respectively, compared to constraints from the corresponding anisotropic BAO measurements without voids and LRG–ELG cross-correlations.

Primordial non-Gaussianity from the completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey – I: Catalogue preparation and systematic mitigation

ABSTRACT We investigate the large-scale clustering of the final spectroscopic sample of quasars from the recently completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). The sample contains 343 708 objects in the redshift range 0.8 < z < 2.2 and 72 667 objects with redshifts 2.2 < z < 3.5, covering an effective area of $4699\, {\rm deg}^{2}$. We develop a neural network-based approach to mitigate spurious fluctuations in the density field caused by spatial variations in the quality of the imaging data used to select targets for follow-up spectroscopy. Simulations are used with the same angular and radial distributions as the real data to estimate covariance matrices, perform error analyses, and assess residual systematic uncertainties. We measure the mean density contrast and cross-correlations of the eBOSS quasars against maps of potential sources of imaging systematics to address algorithm effectiveness, finding that the neural network-based approach outperforms standard linear regression. Stellar density is one of the most important sources of spurious fluctuations, and a new template constructed using data from the Gaia spacecraft provides the best match to the observed quasar clustering. The end-product from this work is a new value-added quasar catalogue with the improved weights to correct for non-linear imaging systematic effects, which will be made public. Our quasar catalogue is used to measure the local-type primordial non-Gaussianity in a companion paper.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: a multitracer analysis in Fourier space for measuring the cosmic structure growth and expansion rate

ABSTRACT We perform a joint BAO and RSD analysis using the eBOSS DR16 LRG and ELG samples in the redshift range of z ∈ [0.6, 1.1], and detect an RSD signal from the cross-power spectrum at a ∼4σ confidence level, i.e., fσ8 = 0.317 ± 0.080 at zeff = 0.77. Based on the chained power spectrum, which is a new development in this work to mitigate the angular systematics, we measure the BAO distances and growth rate simultaneously at two effective redshifts, namely, DM/rd (z = 0.70) = 17.96 ± 0.51, DH/rd (z = 0.70) = 21.22 ± 1.20, fσ8 (z = 0.70) = 0.43 ± 0.05, and DM/rd (z = 0.845) = 18.90 ± 0.78, DH/rd (z = 0.845) = 20.91 ± 2.86, fσ8 (z = 0.845) = 0.30 ± 0.08. Combined with BAO measurements including those from the eBOSS DR16 QSO and Lyman-α sample, our measurement has raised the significance level of a non-zero ΩΛ to ∼11σ. The data product of this work is publicly available at https://github.com/icosmology/eBOSS_DR16_LRGxELG and https://www.sdss.org/science/final-bao-and-rsd-measurements/.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: 1000 multi-tracer mock catalogues with redshift evolution and systematics for galaxies and quasars of the final data release

ABSTRACT We produce 1000 realizations of synthetic clustering catalogues for each type of the tracers used for the baryon acoustic oscillation and redshift space distortion analysis of the Sloan Digital Sky Surveys-iv extended Baryon Oscillation Spectroscopic Survey final data release (eBOSS DR16), covering the redshift range from 0.6 to 2.2, to provide reliable estimates of covariance matrices and test the robustness of the analysis pipeline with respect to observational systematics. By extending the Zel’dovich approximation density field with an effective tracer bias model calibrated with the clustering measurements from the observational data, we accurately reproduce the two- and three-point clustering statistics of the eBOSS DR16 tracers, including their cross-correlations in redshift space with very low computational costs. In addition, we include the gravitational evolution of structures and sample selection biases at different redshifts, as well as various photometric and spectroscopic systematic effects. The agreements on the auto-clustering statistics between the data and mocks are generally within $1\, \sigma$ variances inferred from the mocks, for scales down to a few $h^{-1}\, {\rm Mpc}$ in configuration space, and up to $0.3\, h\, {\rm Mpc}^{-1}$ in Fourier space. For the cross correlations between different tracers, the same level of consistency presents in configuration space, while there are only discrepancies in Fourier space for scales above $0.15\, h\, {\rm Mpc}^{-1}$. The accurate reproduction of the data clustering statistics permits reliable covariances for multi-tracer analysis.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: a catalogue of strong galaxy–galaxy lens candidates

ABSTRACT We spectroscopically detected 838 likely, 448 probable, and 265 possible strong lens candidates within ≈2 million galaxy spectra contained within the extended Baryon Oscillation Spectroscopic Survey (eBOSS) from the sixteenth data release (DR16) of the Sloan Digital Sky Survey (SDSS). We apply the spectroscopic detection method of the Baryon Oscillation Spectroscopic Survey (BOSS) Emission-Line Lens Survey (BELLS) and add Gaussian fit information, grading, additional inspection observables, and additional inspection methods to improve our selection method. We observed 477 candidates with lensing evidence within low-resolution images from both the Legacy survey of SDSS-I/II and the DESI Legacy survey, which is $12{{\ \rm per\ cent}}$ higher than the percentage of BELLS candidates observed with similar lensing evidence. Our search within the latest and improved reductions of the BOSS survey yielded a $20{{\ \rm per\ cent}}$ increase in the number of lens candidates expected from searching all BOSS and eBOSS galaxies. The distribution of target and background redshifts of our candidates is similar to the candidates and confirmed lenses within the BELLS observations. We present our Spectroscopic Identification of Lensing Object candidates in a value-added catalogue in SDSS DR16. The examination of these lens candidates in follow-up high-resolution imaging may yield more than twice the lenses found in previous spectroscopic detection surveys within SDSS, which would extend the results of previous lens surveys within SDSS to higher redshifts, constrain models of mass structures in spiral galaxies, and test if including the identification of possible lensing features within low-resolution images has merit to spectroscopic detection programmes.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1

Abstract We analyse the large-scale clustering in Fourier space of emission line galaxies (ELG) from the Data Release 16 of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey. The ELG sample contains 173,736 galaxies covering 1,170 square degrees in the redshift range 0.6 < z < 1.1. We perform a BAO measurement from the post-reconstruction power spectrum monopole, and study redshift space distortions (RSD) in the first three even multipoles. Photometric variations yield fluctuations of both the angular and radial survey selection functions. Those are directly inferred from data, imposing integral constraints which we model consistently. The full data set has only a weak preference for a BAO feature (1.4σ). At the effective redshift zeff = 0.845 we measure $D_{\rm V}(z_{\rm eff})/r_{\rm drag} = 18.33_{-0.62}^{+0.57}$, with DV the volume-averaged distance and rdrag the comoving sound horizon at the drag epoch. In combination with the RSD measurement, at zeff = 0.85 we find $f\sigma _8(z_{\rm eff}) = 0.289_{-0.096}^{+0.085}$, with f the growth rate of structure and σ8 the normalisation of the linear power spectrum, $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 20.0_{-2.2}^{+2.4}$ and DM(zeff)/rdrag = 19.17 ± 0.99 with DH and DM the Hubble and comoving angular distances, respectively. These results are in agreement with those obtained in configuration space, thus allowing a consensus measurement of fσ8(zeff) = 0.315 ± 0.095, $D_{\rm H}(z_{\rm eff})/r_{\rm drag} = 19.6_{-2.1}^{+2.2}$ and DM(zeff)/rdrag = 19.5 ± 1.0. This measurement is consistent with a flat ΛCDM model with Planck parameters.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from anisotropic clustering analysis of the quasar sample in configuration space between redshift 0.8 and 2.2

ABSTRACT We measure the anisotropic clustering of the quasar sample from Data Release 16 (DR16) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS). A sample of 343 708 spectroscopically confirmed quasars between redshift 0.8 < z < 2.2 are used as tracers of the underlying dark matter field. In comparison with DR14 sample, the final sample doubles the number of objects as well as the survey area. In this paper, we present the analysis in configuration space by measuring the two-point correlation function and decomposing it using the Legendre polynomials. For the full-shape analysis of the Legendre multipole moments, we measure the baryon acoustic oscillation (BAO) distance and the growth rate of the cosmic structure. At an effective redshift of zeff = 1.48, we measure the comoving angular diameter distance DM(zeff)/rdrag = 30.66 ± 0.88, the Hubble distance DH(zeff)/rdrag = 13.11 ± 0.52, and the product of the linear growth rate and the rms linear mass fluctuation on scales of $8 \, h^{-1}\, {\rm Mpc}$, fσ8(zeff) = 0.439 ± 0.048. The accuracy of these measurements is confirmed using an extensive set of mock simulations developed for the quasar sample. The uncertainties on the distance and growth rate measurements have been reduced substantially (∼45 and ∼30 per cent) with respect to the DR14 results. We also perform a BAO-only analysis to cross check the robustness of the methodology of the full-shape analysis. Combining our analysis with the Fourier-space analysis, we arrive at $D^{{\bf c}}_{\rm M}(z_{\rm eff})/r_{\rm drag} = 30.21 \pm 0.79$, $D^{{\bf c}}_{\rm H}(z_{\rm eff})/r_{\rm drag} = 13.23 \pm 0.47$, and $f\sigma _8^{{\bf c}}(z_{\rm eff}) = 0.462 \pm 0.045$.

The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations with Lyα Forests

Abstract We present a measurement of baryonic acoustic oscillations (BAOs) from Lyα absorption and quasars at an effective redshift using the complete extended Baryonic Oscillation Spectroscopic Survey (eBOSS). The 16th and final eBOSS data release (SDSS DR16) contains all data from eBOSS and its predecessor, the Baryonic Oscillation Spectroscopic Survey (BOSS), providing 210,005 quasars with z q > 2.10 that are used to measure Lyα absorption. We measure the BAO scale both in the autocorrelation of Lyα absorption and in its cross-correlation with 341,468 quasars with redshift z q > 1.77. Apart from the statistical gain from new quasars and deeper observations, the main improvements over previous work come from more accurate modeling of physical and instrumental correlations and the use of new sets of mock data. Combining the BAO measurement from the auto- and cross-correlation yields the constraints of the two ratios and , where the error bars are statistical. These results are within 1.5σ of the prediction of the flat-ΛCDM cosmology of Planck (2016). The analysis code, picca, the catalog of the flux transmission field measurements, and the Δχ 2 surfaces are publicly available.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: exploring the halo occupation distribution model for emission line galaxies

ABSTRACT We study the modelling of the halo occupation distribution (HOD) for the eBOSS DR16 emission line galaxies (ELGs). Motivated by previous theoretical and observational studies, we consider different physical effects that can change how ELGs populate haloes. We explore the shape of the average HOD, the fraction of satellite galaxies, their probability distribution function (PDF), and their density and velocity profiles. Our baseline HOD shape was fitted to a semi-analytical model of galaxy formation and evolution, with a decaying occupation of central ELGs at high halo masses. We consider Poisson and sub/super-Poissonian PDFs for satellite assignment. We model both Navarro–Frenk–White and particle profiles for satellite positions, also allowing for decreased concentrations. We model velocities with the virial theorem and particle velocity distributions. Additionally, we introduce a velocity bias and a net infall velocity. We study how these choices impact the clustering statistics while keeping the number density and bias fixed to that from eBOSS ELGs. The projected correlation function, wp, captures most of the effects from the PDF and satellites profile. The quadrupole, ξ2, captures most of the effects coming from the velocity profile. We find that the impact of the mean HOD shape is subdominant relative to the rest of choices. We fit the clustering of the eBOSS DR16 ELG data under different combinations of the above assumptions. The catalogues presented here have been analysed in companion papers, showing that eBOSS RSD+BAO measurements are insensitive to the details of galaxy physics considered here. These catalogues are made publicly available.

Removing imaging systematics from galaxy clustering measurements with Obiwan: application to the SDSS-IV extended Baryon Oscillation Spectroscopic Survey emission-line galaxy sample

ABSTRACT This work presents the application of a new tool, Obiwan, which uses image simulations to determine the selection function of a galaxy redshift survey and calculate three-dimensional (3D) clustering statistics. Obiwan relies on a forward model of the process by which images of the night sky are transformed into a 3D large-scale structure catalogue, and offers several advantages over more traditional map-based techniques – such as operating on individual exposures and adopting a maximum likelihood approach. The photometric pipeline automatically detects and models galaxies and then generates a catalogue of such galaxies with detailed information for each one of them, including their location, redshift, and so on. Systematic biases in the imaging data are therefore imparted into the catalogues and must be accounted for in any scientific analysis of their information content. Obiwan simulates this process for samples selected from the Legacy Surveys imaging data. This imaging data will be used to select target samples for the next-generation Dark Energy Spectroscopic Instrument (DESI) experiment. Here, we apply Obiwan to a portion of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey emission-line galaxies (ELGs). Systematic biases in the data are clearly identified and removed. We compare the 3D clustering results to those obtained by the map-based approach applied to the complete eBOSS Data Release 16 (DR16) sample. We find the results are consistent, thereby validating the eBOSS DR16 ELG catalogues, which is used to obtain cosmological results.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1

ABSTRACT We present the cosmological analysis of the configuration-space anisotropic clustering in the completed Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 galaxy sample. This sample consists of luminous red galaxies (LRGs) spanning the redshift range 0.6 < $z$ < 1, at an effective redshift of $z$eff = 0.698. It combines 174 816 eBOSS and 202 642 BOSS LRGs. We extract and model the baryon acoustic oscillation (BAO) and redshift-space distortion (RSD) features from the galaxy two-point correlation function to infer geometrical and dynamical cosmological constraints. The adopted methodology is extensively tested on a set of realistic simulations. The correlations between the inferred parameters from the BAO and full-shape correlation function analyses are estimated. This allows us to derive joint constraints on the three cosmological parameter combinations: DM($z$)/rd, DH($z$)/rd, and fσ8($z$), where DM is the comoving angular diameter distance, DH is the Hubble distance, rd is the comoving BAO scale, f is the linear growth rate of structure, and σ8 is the amplitude of linear matter perturbations. After combining the results with those from the parallel power spectrum analysis of Gil-Marin et al., we obtain the constraints: DM/rd = 17.65 ± 0.30, DH/rd = 19.77 ± 0.47, and fσ8 = 0.473 ± 0.044. These measurements are consistent with a flat Lambda cold dark matter model with standard gravity.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: BAO and RSD measurements from the anisotropic power spectrum of the quasar sample between redshift 0.8 and 2.2

ABSTRACT We measure the clustering of quasars of the final data release (DR16) of eBOSS. The sample contains $343\, 708$ quasars between redshifts 0.8 ≤ z ≤ 2.2 over $4699\, \mathrm{deg}^2$. We calculate the Legendre multipoles (0,2,4) of the anisotropic power spectrum and perform a BAO and a Full-Shape (FS) analysis at the effective redshift zeff = 1.480. The errors include systematic errors that amount to 1/3 of the statistical error. The systematic errors comprise a modelling part studied using a blind N-body mock challenge and observational effects studied with approximate mocks to account for various types of redshift smearing and fibre collisions. For the BAO analysis, we measure the transverse comoving distance DM(zeff)/rdrag = 30.60 ± 0.90 and the Hubble distance DH(zeff)/rdrag = 13.34 ± 0.60. This agrees with the configuration space analysis, and the consensus yields: DM(zeff)/rdrag = 30.69 ± 0.80 and DH(zeff)/rdrag = 13.26 ± 0.55. In the FS analysis, we fit the power spectrum using a model based on Regularised Perturbation Theory, which includes redshift space distortions and the Alcock–Paczynski effect. The results are DM(zeff)/rdrag = 30.68 ± 0.90 and DH(zeff)/rdrag = 13.52 ± 0.51 and we constrain the linear growth rate of structure f(zeff)σ8(zeff) = 0.476 ± 0.047. Our results agree with the configuration space analysis. The consensus analysis of the eBOSS quasar sample yields: DM(zeff)/rdrag = 30.21 ± 0.79, DH(zeff)/rdrag = 3.23 ± 0.47, and f(zeff)σ8(zeff) = 0.462 ± 0.045 and is consistent with a flat ΛCDM cosmological model using Planck results.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale structure catalogues for cosmological analysis

ABSTRACT We present large-scale structure catalogues from the completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). Derived from Sloan Digital Sky Survey (SDSS) IV Data Release 16 (DR16), these catalogues provide the data samples, corrected for observational systematics, and random positions sampling the survey selection function. Combined, they allow large-scale clustering measurements suitable for testing cosmological models. We describe the methods used to create these catalogues for the eBOSS DR16 Luminous Red Galaxy (LRG) and Quasar samples. The quasar catalogue contains 343 708 redshifts with 0.8 < z < 2.2 over 4808 deg2. We combine 174 816 eBOSS LRG redshifts over 4242 deg2 in the redshift interval 0.6 < z < 1.0 with SDSS-III BOSS LRGs in the same redshift range to produce a combined sample of 377 458 galaxy redshifts distributed over 9493 deg2. Improved algorithms for estimating redshifts allow that 98 per cent of LRG observations result in a successful redshift, with less than one per cent catastrophic failures (Δz > 1000 km s−1). For quasars, these rates are 95 and 2 per cent (with Δz > 3000 km s−1). We apply corrections for trends between the number densities of our samples and the properties of the imaging and spectroscopic data. For example, the quasar catalogue obtains a χ2/DoF = 776/10 for a null test against imaging depth before corrections and a χ2/DoF= 6/8 after. The catalogues, combined with careful consideration of the details of their construction found here-in, allow companion papers to present cosmological results with negligible impact from observational systematic uncertainties.

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic power spectrum between redshifts 0.6 and 1.0

ABSTRACT We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 luminous red galaxy sample (DR16 eBOSS LRG) in combination with the high redshift tail of the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12 BOSS CMASS). We measure the redshift space distortions (RSD) and also extract the longitudinal and transverse baryonic acoustic oscillation (BAO) scale from the anisotropic power spectrum signal inferred from 377 458 galaxies between redshifts 0.6 and 1.0, with the effective redshift of zeff = 0.698 and effective comoving volume of $2.72\, {\rm Gpc}^3$. After applying reconstruction, we measure the BAO scale and infer DH(zeff)/rdrag = 19.30 ± 0.56 and DM(zeff)/rdrag = 17.86 ± 0.37. When we perform an RSD analysis on the pre-reconstructed catalogue on the monopole, quadrupole, and hexadecapole we find, DH(zeff)/rdrag = 20.18 ± 0.78, DM(zeff)/rdrag = 17.49 ± 0.52 and fσ8(zeff) = 0.454 ± 0.046. We combine both sets of results along with the measurements in configuration space and report the following consensus values: DH(zeff)/rdrag = 19.77 ± 0.47, DM(zeff)/rdrag = 17.65 ± 0.30 and fσ8(zeff) = 0.473 ± 0.044, which are in full agreement with the standard ΛCDM and GR predictions. These results represent the most precise measurements within the redshift range 0.6 ≤ z ≤ 1.0 and are the culmination of more than 8 yr of SDSS observations.

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

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 optimise 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 $f\sigma_8$ and parameters controlling the anisotropic projection of the cosmological perturbations. We measure $f \sigma_8(z=1.52)=0.43 \pm 0.05 $ and $df\sigma_8/dz (z=1.52)= - 0.16 \pm 0.08$, consistent with the expectation for a $\Lambda$CDM cosmology as constrained by the Planck experiment.

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

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 EZ mocks, and apply our pipeline to the eBOSS DR14Q sample in the redshift range of $0.8<z<2.2$. We report a joint measurement of $f\sigma_8$ and two-dimensional BAO parameters $D_{\rm A}$ and $H$ at four effective redshifts of $z_{\rm eff}=0.98, 1.23, 1.52$ and $1.94$, and provide the full data covariance matrix. Using our measurement combined with BOSS DR12, MGS and 6dFGS BAO measurements, we find that the existence of dark energy is supported by observations at a $7.4\sigma$ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be $\gamma=0.580\pm0.082$, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

The SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations at Redshift of 0.72 with the DR14 Luminous Red Galaxy Sample

Abstract The extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 sample includes 80,118 luminous red galaxies (LRGs). By combining these galaxies with the high-redshift tail of the BOSS galaxy sample, we form a sample of LRGs at an effective redshift z = 0.72, covering an effective volume of 0.9 Gpc3. We account for spurious fluctuations caused by targeting and by redshift failures, which were validated on a set of mock catalogs. This analysis is sufficient to provide a 2.5% measurement of spherically averaged baryon acoustic oscillations (BAO), Mpc, at 2.8σ of significance. Together with the recent quasar-based BAO measurement at z = 1.5 and forthcoming emission line galaxy–based measurements, this measurement demonstrates that eBOSS is fulfilling its remit of extending the range of redshifts covered by such measurements, laying the groundwork for forthcoming surveys such as the Dark Energy Spectroscopic Survey and Euclid.

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

We present the clustering measurements of quasars in configuration space based on the Data Release 14 (DR14) of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey. This dataset includes 148,659 quasars spread over the redshift range $0.8\leq z \leq 2.2$ and spanning 2112.9 square degrees. We use the Convolution Lagrangian Perturbation Theory (CLPT) approach with a Gaussian Streaming (GS) model for the redshift space distortions of the correlation function and demonstrate its applicability for dark matter halos hosting eBOSS quasar tracers. At the effective redshift $z_{\rm eff} = 1.52$, we measure the linear growth rate of structure $f\sigma_{8}(z_{\rm eff})= 0.426 \pm 0.077$, the expansion rate $H(z_{\rm eff})= 159^{+12}_{-13}(r_{s}^{\rm fid}/r_s){\rm km.s}^{-1}.{\rm Mpc}^{-1}$, and the angular diameter distance $D_{A}(z_{\rm eff})=1850^{+90}_{-115}\,(r_s/r_{s}^{\rm fid}){\rm Mpc}$, where $r_{s}$ is the sound horizon at the end of the baryon drag epoch and $r_{s}^{\rm fid}$ is its value in the fiducial cosmology. The quoted errors include both systematic and statistical contributions. The results on the evolution of distances are consistent with the predictions of flat $\Lambda$-Cold Dark Matter ($\Lambda$-CDM) cosmology with Planck parameters, and the measurement of $f\sigma_{8}$ extends the validity of General Relativity (GR) to higher redshifts($z>1$) This paper is released with companion papers using the same sample. The results on the cosmological parameters of the studies are found to be in very good agreement, providing clear evidence of the complementarity and of the robustness of the first full-shape clustering measurements with the eBOSS DR14 quasar sample.