Searcharxiv⌕ Search

arXiv subjects

Ashley J. Ross

Publications and source records attributed to Ashley J. Ross.

At least 73 records · Page 4Linked to original sources
arXiv2020

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Pairwise-Inverse-Probability and Angular Correction for Fibre Collisions in Clustering Measurements

The completed eBOSS catalogues contain redshifts of 344080 QSOs over 0.8<z<2.2 covering 4808 deg$^2$, 174816 LRGs over 0.6<z<1.0 covering 4242 deg$^2$ and 173736 ELGs over 0.6<z<1.1 covering 1170 deg$^2$ in order to constrain the expansion history of the Universe and the growth rate of structure through clustering measurements. Mechanical limitations of the fibre-fed spectrograph on the Sloan telescope prevent two fibres being placed closer than 62", the fibre-collision scale, in a single pass of the instrument on the sky. These `fibre collisions' strongly correlate with the intrinsic clustering of targets and can bias measurements of the two-point correlation function resulting in a systematic error on the inferred values of the cosmological parameters. We combine the new techniques of pairwise-inverse-probability weighting and the angular up-weighting to correct the clustering measurements for the effect of fibre collisions. Using mock catalogues we show that our corrections provide unbiased measurements, within data precision, of both the projected correlation function $w_p$ and the multipoles $ξ^l$ of the redshift-space correlation functions down to 0.1Mpc/h, regardless of the tracer type. We apply the corrections to the eBOSS DR16 catalogues. We find that, on scales greater than s~20Mpc/h for $ξ^l$, as used to make BAO and large-scale RSD measurements, approximate methods such as Nearest-Neighbour up-weighting are sufficiently accurate given the statistical errors of the data. Using the PIP method, for the first time for a spectroscopic program of the Sloan Digital Sky Survey we are able to successfully access the 1-halo term in the 3D clustering measurements down to ~0.1Mpc/h scales. Our results will therefore allow studies that use the small-scale clustering measurements to strengthen the constraints on both cosmological parameters and the halo-occupation distribution models.

astro-ph.CO↗
arXiv2020

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale Structure Catalogues and Measurement of the isotropic BAO between redshift 0.6 and 1.1 for the Emission Line Galaxy Sample

We present the Emission Line Galaxy (ELG) sample of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) from the Sloan Digital Sky Survey IV Data Release 16 (DR16). After describing the observations and redshift measurement for the 269,243 observed ELG spectra over 1170 deg$^2$, we present the large-scale structure catalogues, which are used for the cosmological analysis. These catalogues contain 173,736 reliable spectroscopic redshifts between 0.6 and 1.1, along with the associated random catalogues quantifying the extent of observations, and the appropriate weights to correct for non-cosmological fluctuations. We perform a spherically averaged baryon acoustic oscillations (BAO) measurement in configuration space, with density field reconstruction: the data 2-point correlation function shows a feature consistent with that of the BAO, providing a 3.2-percent measurement of the spherically averaged BAO distance $D_V(z_{\rm eff})/r_{\rm drag} = 18.23\pm 0.58$ at the effective redshift $z_{\rm eff}=0.845$.

astro-ph.CO↗
arXiv2020

The Sloan Digital Sky Survey Quasar Catalog: Sixteenth Data Release

We present the final Sloan Digital Sky Survey IV (SDSS-IV) quasar catalog from Data Release 16 of the extended Baryon Oscillation Spectroscopic Survey (eBOSS). This catalog comprises the largest selection of spectroscopically confirmed quasars to date. The full catalog includes two sub-catalogs: a "superset" of all SDSS-IV/eBOSS objects targeted as quasars containing 1,440,615 observations and a quasar-only catalog containing 750,414 quasars, including 225,082 new quasars appearing in an SDSS data release for the first time, as well as known quasars from SDSS-I/II/III. We present automated identification and redshift information for these quasars alongside data from visual inspections for 320,161 spectra. The quasar-only catalog is estimated to be 99.8% complete with 0.3% to 1.3% contamination. Automated and visual inspection redshifts are supplemented by redshifts derived via principal component analysis and emission lines. We include emission line redshifts for H$α$, H$β$, Mg II, C III], C IV, and Ly$α$. Identification and key characteristics generated by automated algorithms are presented for 99,856 Broad Absorption Line quasars and 35,686 Damped Lyman Alpha quasars. In addition to SDSS photometric data, we also present multi-wavelength data for quasars from GALEX, UKIDSS, WISE, FIRST, ROSAT/2RXS, XMM-Newton, and Gaia. Calibrated digital optical spectra for these quasars can be obtained from the SDSS Science Archive Server.

astro-ph.GA↗
arXiv2020

Multi-tracer extension of the halo model: probing quenching and conformity in eBOSS

We develop a new Multi-Tracer Halo Occupation Distribution (\texttt{MTHOD}) framework for the galaxy distribution and apply it to the extended Baryon Oscillation Spectroscopic Survey (eBOSS) final data between $z=0.7-1.1$. We obtain a best fit \mthod\, for each tracer and describe the host halo properties of these galaxies. The mean halo masses for LRGs, ELGs and QSOs are found to be $1.9 \times 10^{13} \msolaroh$, $1.1 \times 10^{12} \msolaroh$ and $5 \times 10^{12} \msolaroh$ respectively in the eBOSS data. We use the \texttt{MTHOD} framework to create mock galaxy catalogues and predict auto- and cross-correlation functions for all the tracers. Comparing these results with data, we investigate galactic conformity, the phenomenon whereby the properties of neighbouring galaxies are mutually correlated in a manner that is not captured by the basic halo model. We detect \textsl{1-halo} conformity at more than 3$σ$ statistical significance, while obtaining upper limit on \textsl{2-halo} conformity. We also look at the environmental dependence of the galaxy quenching efficiency and find that halo mass driven quenching successfully explains the behaviour in high density regions, but it fails to describe the quenching efficiency in low density regions. In particular, we show that the quenching efficiency in low density filaments is higher in the observed data, as compared to the prediction of the \mthod\ with halo mass driven quenching. The mock galaxy catalogue constructed in this paper is publicly available on https://www.roe.ac.uk/~salam/MTHOD/ .

astro-ph.CO↗
arXiv2020

The clustering of LRGs in the DECaLS DR8 footprint: distance constraints from baryon acoustic oscillations using photometric redshifts

A photometric redshift sample of Luminous Red Galaxies (hereafter LRGs) obtained from The DECam Legacy Survey (DECaLS) is analysed to probe cosmic distances by exploiting the wedge approach of the two-point correlation function. Although the cosmological information is highly contaminated by the uncertainties existing in the photometric redshifts from the galaxy map, an angular diameter distance can be probed at the perpendicular configuration in which the measured correlation function is minimally contaminated. An ensemble of wedged correlation functions selected up to a given threshold based on having the least contamination was studied in the previous work (arXiv:1903.09651v2 [astro-ph.CO]) using simulations, and the extracted cosmological information was unbiased within this threshold. We apply the same methodology for analysing the LRG sample from DECaLS which will provide the optical imaging for targeting two-thirds of the DESI footprint and measure the angular diameter distances at $z=0.69$ and $z=0.87$ to be $D_{A}(0.697)=(1499 \pm 77\,\mathrm{Mpc})(r_{d}/r_{d,fid})$ and $D_{A}(0.874)=(1680 \pm 109\,\mathrm{Mpc})(r_{d}/r_{d,fid})$ with a fractional error of 5.14% and 6.48% respectively. We obtain a value of $H_{0}=67.59\pm5.52$ km/s/Mpc which supports the $H_0$ measured by all other BAO results and is consistent with $Λ$CDM model.

astro-ph.CO↗
arXiv2020

Improving Galaxy Clustering Measurements with Deep Learning: analysis of the DECaLS DR7 data

Robust measurements of cosmological parameters from galaxy surveys rely on our understanding of systematic effects that impact the observed galaxy density field. In this paper we present, validate, and implement the idea of adopting the systematics mitigation method of Artificial Neural Networks for modeling the relationship between the target galaxy density field and various observational realities including but not limited to Galactic extinction, seeing, and stellar density. Our method by construction allows a wide class of models and alleviates over-training by performing k-fold cross-validation and dimensionality reduction via backward feature elimination. By permuting the choice of the training, validation, and test sets, we construct a selection mask for the entire footprint. We apply our method on the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Emission Line Galaxies (ELGs) selection from the Dark Energy Camera Legacy Survey (DECaLS) Data Release 7 and show that the spurious large-scale contamination due to imaging systematics can be significantly reduced by up-weighting the observed galaxy density using the selection mask from the neural network and that our method is more effective than the conventional linear and quadratic polynomial functions. We perform extensive analyses on simulated mock datasets with and without systematic effects. Our analyses indicate that our methodology is more robust to overfitting compared to the conventional methods. This method can be utilized in the catalog generation of future spectroscopic galaxy surveys such as eBOSS and Dark Energy Spectroscopic Instrument (DESI) to better mitigate observational systematics.

astro-ph.CO↗
arXiv2019

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 $σ_{f^{\rm loc}_{\rm NL}}\simeq 5\text{-}8$ using optimal methods and full range of scales.

astro-ph.CO↗
arXiv2018

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 $fσ_8$ 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 $7.4σ$ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be $γ=0.580\pm0.082$, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

astro-ph.CO↗
arXiv2018

Unbiased clustering estimates with the DESI fibre assignment

The Emission Line Galaxy survey made by the Dark Energy Spectroscopic Instrument (DESI) survey will be created from five passes of the instrument on the sky. On each pass, the constrained mobility of the ends of the fibres in the DESI focal plane means that the angular-distribution of targets that can be observed is limited. Thus, the clustering of samples constructed using a limited number of passes will be strongly affected by missing targets. In two recent papers, we showed how the effect of missing galaxies can be corrected when calculating the correlation function using a weighting scheme for pairs. Using mock galaxy catalogues we now show that this method provides an unbiased estimator of the true correlation function for the DESI survey after any number of passes. We use multiple mocks to determine the expected errors given one to four passes, compared to an idealised survey observing an equivalent number of randomly selected targets. On BAO scales, we find that the error is a factor 2 worse after one pass, but that after three or more passes, the errors are very similar. Thus we find that the fibre assignment strategy enforced by the design of DESI will not affect the cosmological measurements to be made by the survey, and can be removed as a potential risk for this experiment.

astro-ph.CO↗
arXiv2018

The Commissioning Instrument for the Dark Energy Spectroscopic Instrument

We describe the design of the Commissioning Instrument for the Dark Energy Spectroscopic Instrument (DESI). DESI will obtain spectra over a 3 degree field of view using the 4-meter Mayall Telescope at Kitt Peak, AZ. In order to achieve the required image quality over this field of view, a new optical corrector is being installed at the Mayall Telescope. The Commissioning Instrument is designed to characterize the image quality of the new optical system. The Commissioning Instrument has five commercial cameras; one at the center of the focal surface and four near the periphery of the field and at the cardinal directions. There are also 22 illuminated fiducials, distributed throughout the focal surface, that will be used to test the system that will map between the DESI fiber positioners and celestial coordinates. We describe how the commissioning instrument will perform commissioning tasks for the DESI project and thereby eliminate risks.

astro-ph.IM↗
arXiv2018

Low Redshift Baryon Acoustic Oscillation Measurement from the Reconstructed 6-degree Field Galaxy Survey

Low redshift measurements of Baryon Acoustic Oscillations (BAO) test the late time evolution of the Universe and are a vital probe of Dark Energy. Over the past decade both the 6-degree Field Galaxy Survey (6dFGS) and Sloan Digital Sky Survey (SDSS) have provided important distance constraints at $z < 0.3$. In this paper we re-evaluate the cosmological information from the BAO detection in 6dFGS making use of HOD populated COLA mocks for a robust covariance matrix and taking advantage of the now commonly implemented technique of density field reconstruction. For the 6dFGS data, we find consistency with the previous analysis, and obtain an isotropic volume averaged distance measurement of $D_{V}(z_{\mathrm{eff}}=0.097) = 372\pm17(r_{s}/r_{s}^{\mathrm{fid}})\,\mathrm{Mpc}$, which has a non-Gaussian likelihood outside the $1σ$ region. We combine our measurement from both the post-reconstruction clustering of 6dFGS and SDSS MGS offering the most robust constraint to date in this redshift regime, $D_{V}(z_{\mathrm{eff}}=0.122)=539\pm17(r_{s}/r^{\mathrm{fid}}_{s})\,\mathrm{Mpc}$. These measurements are consistent with standard $Λ\mathrm{CDM}$ and after fixing the standard ruler using a Planck prior on $Ω_{m}h^{2}$, the joint analysis gives $H_{0}=64.0\pm3.5\,\mathrm{kms}^{-1}\mathrm{Mpc}^{-1}$. In the near future both the Taipan Galaxy Survey and the Dark Energy Spectroscopic Instrument (DESI) will improve this measurement to $1\%$ at low redshift.

astro-ph.CO↗
arXiv2018

The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: theoretical systematics and Baryon Acoustic Oscillations in the galaxy correlation function

We investigate the potential sources of theoretical systematics in the anisotropic Baryon Acoustic Oscillation (BAO) distance scale measurements from the clustering of galaxies in configuration space using the final Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS). We perform a detailed study of the impact on BAO measurements from choices in the methodology such as fiducial cosmology, clustering estimators, random catalogues, fitting templates, and covariance matrices. The theoretical systematic uncertainties in BAO parameters are found to be 0.002 in the isotropic dilation $α$ and 0.003 in the quadrupolar dilation $ε$. The leading source of systematic uncertainty is related to the reconstruction techniques. Theoretical uncertainties are sub-dominant compared with the statistical uncertainties for BOSS survey, accounting $0.2σ_{stat}$ for $α$ and $0.25σ_{stat}$ for $ε$ ($σ_{α,stat} \sim$0.010 and $σ_{ε,stat}\sim$ 0.012 respectively). We also present BAO-only distance scale constraints from the anisotropic analysis of the correlation function. Our constraints on the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$, including both statistical and theoretical systematic uncertainties, are 1.5\% and 2.8\% at $z_{\rm eff}=0.38$, 1.4\% and 2.4\% at $z_{\rm eff}=0.51$, and 1.7\% and 2.6\% at $z_{\rm eff}=0.61$. This paper is part of a set that analyzes the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are cross-checked with other BAO analysis in \citet{Acacia16}. The systematic error budget concerning the methodology on post-reconstruction BAO analysis presented here is used in \citet{Acacia16} to produce the final cosmological constraints from BOSS.

astro-ph.CO↗
arXiv2018

A Radial Measurement of the Galaxy Tidal Alignment Magnitude with BOSS Data

The anisotropy of galaxy clustering in redshift space has long been used to probe the rate of growth of cosmological perturbations. However, if galaxies are aligned by large-scale tidal fields, then a sample with an orientation-dependent selection effect has an additional anisotropy imprinted onto its correlation function. We use the LOWZ and CMASS catalogs of SDSS-III BOSS Data Release 12 to divide galaxies into two sub-samples based on their offset from the Fundamental Plane, which should be correlated with orientation. These sub-samples must trace the same underlying cosmology, but have opposite orientation-dependent selection effects. We measure the clustering parameters of each sub-sample and compare them in order to calculate the dimensionless parameter $B$, a measure of how strongly galaxies are aligned by gravitational tidal fields. We found that for CMASS (LOWZ), the measured $B$ was $-0.024 \pm 0.015$ ($-0.030 \pm 0.016$). This result can be compared to the theoretical predictions of Hirata 2009, who argued that since galaxy formation physics does not depend on the direction of the observer, the same intrinsic alignment parameters that describe galaxy-ellipticity correlations should also describe intrinsic alignments in the radial direction. We find that the ratio of observed to theoretical values is $0.51\pm 0.32$ ($0.77\pm0.41$) for CMASS (LOWZ). We combine the results to obtain a total ${\rm {Obs}/{Theory}} = 0.61\pm 0.26$. This measurement constitutes evidence (between 2 and 3$σ$) for radial intrinsic alignments, and is consistent with theoretical expectations ($<2σ$ difference).

astro-ph.CO↗
arXiv2018

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

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 $α(z_{\rm eff})$ by 17\%. 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.

astro-ph.CO↗
arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: Measuring the anisotropic Baryon Acoustic Oscillations with redshift weights

We present an anisotropic analysis of Baryon Acoustic Oscillation (BAO) signal from the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample. The sample consists of 147,000 quasars distributed over a redshift range of $0.8 < z < 2.2$. 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 $D_M$ at $z = 2.2$ and Hubble parameter $H$ at $z=0.8$. We parameterize the distance-redshift relation, relative to a fiducial model, as a quadratic expansion. 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 $D_M(z=1) = 3405\pm305 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=1) = 120.7\pm 7.3 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$ and $D_M(z=2) = 5325\pm249 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=2) = 189.9\pm 32.9 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$. 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.

astro-ph.CO↗
arXiv2018

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 $fσ_{8}(z_{\rm eff})= 0.426 \pm 0.077$, 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 $Λ$-Cold Dark Matter ($Λ$-CDM) cosmology with Planck parameters, and the measurement of $fσ_{8}$ 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.

astro-ph.CO↗
arXiv2018

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 $0.8<z<2.2$

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 deg$^2$. We constrain the logarithmic growth of structure times the amplitude of dark matter density fluctuations, $fσ_8$, and the Alcock-Paczynski dilation scales which allow constraints to be placed on the angular diameter distance $D_A(z)$ and the Hubble $H(z)$ parameter. At the effective redshift of $z_{\rm eff}=1.52$, $fσ_8(z_{\rm eff})=0.420\pm0.076$, $H(z_{\rm eff})=[162\pm 12]\, (r_s^{\rm fid}/r_s)\,{\rm km\, s}^{-1}{\rm Mpc}^{-1}$, and $D_A(z_{\rm eff})=[1.85\pm 0.11]\times10^3\,(r_s/r_s^{\rm fid})\,{\rm Mpc}$, where $r_s$ 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 ($Λ$CDM) 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.

astro-ph.CO↗