arXiv subjects

Will J. Percival

Publications and source records attributed to Will J. Percival.

At least 109 records · Page 6Linked to original sources

arXiv2019

Anisotropic halo assembly bias and redshift-space distortions

We study the effect of large-scale tidal fields on internal halo properties using a set of N-body simulations. We measure significant cross-correlations between large-scale tidal fields and several non-scalar halo properties: shapes, velocity dispersion, and angular momentum. Selection effects that couple to these non-scalar halo properties can produce anisotropic clustering even in real-space. We investigate the size of this effect and show that it can produce a non-zero quadrupole similar in size to the one generated by linear redshift-space distortions (RSD). Finally, we investigate the clustering properties of halos identified in redshift-space and find enormous deviations from the standard linear RSD model, again caused by anisotropic assembly bias. These effects could contaminate the values of cosmological parameters inferred from the observed redshift-space clustering of galaxies, groups, or 21cm emission from atomic hydrogen, if their selection depends on properties affected by halo assembly bias. We briefly discuss ways in which this effect can be measured in existing and future large-scale structure surveys.

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arXiv2019

Beyond BAO: improving cosmological constraints from BOSS with measurement of the void-galaxy cross-correlation

We present a measurement of the anisotropic void-galaxy cross-correlation function in the CMASS galaxy sample of the BOSS DR12 data release. We perform a joint fit to the data for redshift space distortions (RSD) due to galaxy peculiar velocities and anisotropies due to the Alcock-Paczynski (AP) effect, for the first time using a velocity field reconstruction technique to remove the complicating effects of RSD in the void centre positions themselves. Fits to the void-galaxy function give a 1% measurement of the AP parameter combination $D_A(z)H(z)/c = 0.4367\pm 0.0045$ at redshift $z=0.57$, where $D_A$ is the angular diameter distance and $H$ the Hubble parameter, exceeding the precision obtainable from baryon acoustic oscillations (BAO) by a factor of ~3.5 and free of systematic errors. From voids alone we also obtain a 10% measure of the growth rate, $fσ_8(z=0.57)=0.501\pm0.051$. The parameter degeneracies are orthogonal to those obtained from galaxy clustering. Combining void information with that from BAO and galaxy RSD in the same CMASS sample, we measure $D_A(0.57)/r_s=9.383\pm 0.077$ (at 0.8% precision), $H(0.57)r_s=(14.05\pm 0.14)\;10^3$ kms$^{-1}$Mpc$^{-1}$ (1%) and $fσ_8=0.453\pm0.022$ (4.9%), consistent with cosmic microwave background (CMB) measurements from Planck. These represent a factor \sim2 improvement in precision over previous results through the inclusion of void information. Fitting a flat cosmological constant $Λ$CDM model to these results in combination with Planck CMB data, we find up to an 11% reduction in uncertainties on $H_0$ and $Ω_m$ compared to use of the corresponding BOSS consensus values. Constraints on extended models with non-flat geometry and a dark energy of state that differs from $w=-1$ show an even greater improvement.

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arXiv2019

The Impact of the Fiducial Cosmology Assumption on BAO Cosmological Parameter Inference

Standard analysis pipelines for measurements of Baryon Acoustic Oscillations (BAO) in galaxy surveys make use of a fiducial cosmological model to guide the data compression required to transform from observed redshifts and angles to the measured angular and radial BAO peak positions. In order to remove any dependence on the fiducial cosmology from the results, all models compared to the data should mimic the compression and its dependence on the fiducial model. In practice, approximations are made when testing models: (1) There is assumed to be no residual dependence on the fiducial cosmology after reconstruction, (2) differences in the distance--redshift relationship are assumed to match a linear scaling, and (3) differences in clustering between true and fiducial models are assumed to be removed by the free parameters used to null the non-BAO signal. We test these approximations using the current standard measurement procedure with a set of halo catalogs from the {\sc Aemulus} suite of $N$-body simulations, which span a range of $w\mathrm{CDM}$ cosmological models. We focus on reconstruction of the primordial BAO and locating the BAO. For the range of $w\mathrm{CDM}$ cosmologies covered by the {\sc Aemulus} suite, we find no evidence for systematic errors in the measured BAO shift parameters $α_{\parallel}$ and $α_{\bot}$ to $< 0.1\%$. However, the measured errors $σ_{α_{\parallel}}$ and $σ_{α_{\bot}}$ show a notable absolute increase by up to $+0.001$ and $+0.002$ respectively in the case that the fiducial cosmology does not match the truth. These effects on the inferred BAO scale will be important given the precision of measurements expected from future surveys including DESI, Euclid, and WFIRST.

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arXiv2019

Cosmological Inference from Galaxy-Clustering Power Spectrum: Gaussianization and Covariance Decomposition

Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of overdensity modes. However, this assumption cannot hold on the largest scales where the number of modes is low. Whilst more accurate distributions have previously been developed in idealized cases, we derive a procedure suitable for analysing measured monopole power spectra with window effects, stochastic shot noise, and the dependence of the covariance matrix on the model being fitted all taken into account. A data transformation is proposed to give an approximately Gaussian likelihood, with a variance--correlation decomposition of the covariance matrix to account for its cosmological dependence. By comparing with the modified-$t$ likelihood derived under the usual normality assumption, we find in numerical tests that our new procedure gives more accurate constraints on the local non-Gaussianity parameter $f_\mathrm{NL}$, which is sensitive to the large-scale power. A simple data analysis pipeline is provided for straightforward application of this new approach in preparation for forthcoming large galaxy surveys such as DESI and Euclid.

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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.

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arXiv2019

Cosmology with the MaunaKea Spectroscopic Explorer

This document summarizes the science cases related to cosmology studies with the MaunaKea Spectroscopic Explorer (MSE), a highly-multiplexed (4332 fibers), wide FOV (1.5 sq deg), large aperture (11.25 m in diameter), optical/NIR (360nm to 1300nm) facility. The MSE High-z Cosmology Survey is designed to probe a large volume of the Universe with a galaxy density sufficient to measure the extremely-large-scale density fluctuations required to explore primordial non-Gaussianity and therefore inflation. We expect a measurement of the local parameter $f_{NL}$ to a precision $σ(f_{NL}) = 1.8$. Combining the MSE High-z Cosmology Survey data with data from a next generation CMB stage 4 experiment and existing DESI data will provide the first $5σ$ confirmation of the neutrino mass hierarchy from astronomical observations. In addition, the Baryonic Acoustic Oscillations (BAO) observed within the sample will provide measurements of the distance-redshift relationship in six different redshift bins between $z=1.6$ and 4.0, each with an accuracy of $\sim0.6\%$. The simultaneous measurements of Redshift Space Distortions (RSD) constrain the amplitude of the fluctuations, at a level ranging from $1.9\%$ to $3.6\%$. The proposed survey covers 10,000 ${\rm deg}^2$, measuring redshifts for three classes of target objects: Emission Line Galaxies (ELGs) with $1.6<z<2.4$, Lyman Break Galaxies (LBGs) with $2.4<z<4.0$, and quasars $2.1<z<3.5$. The ELGs and LBGs will be used as direct tracers of the underlying density field, while the Lyman-$α$ forests in the quasar spectra will be utilized to probe structure. Exposures of duration 1,800sec will guarantee a redshift determination efficiency of $90\%$ for ELGS and at least $50\%$ for LBGs. The survey will represent 100 nights per year for a 5-year MSE program. Finally, three ideas for additional projects of cosmological interest are proposed.

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arXiv2019

Correcting for Fibre Assignment Incompleteness in the DESI Bright Galaxy Survey

The Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey (BGS) will be a survey of bright, low redshift galaxies, which is planned to cover an area of ~14,000 sq deg in 3 passes. Each pass will cover the survey area with ~2000 pointings, each of area ~8 sq deg. The BGS is currently proposed to consist of a bright high priority sample to an r-band magnitude limit r ~ 19.5, with a fainter low priority sample to r ~ 20. The geometry of the DESI fibre positioners in the focal plane of the telescope affects the completeness of the survey, and has a non-trivial impact on clustering measurements. Using a BGS mock catalogue, we show that completeness due to fibre assignment primarily depends on the surface density of galaxies. Completeness is high (>95%) in low density regions, but very low (<10%) in the centre of massive clusters. We apply the pair inverse probability (PIP) weighting correction to clustering measurements from a BGS mock which has been through the fibre assignment algorithm. This method is only unbiased if it is possible to observe every galaxy pair. To facilitate this, we randomly promote a small fraction of the fainter sample to be high priority, and dither the set of tile positions by a small angle. We show that inverse pair weighting combined with angular upweighting provides an unbiased correction to galaxy clustering measurements for the complete 3 pass survey, and also after 1 pass, which is highly incomplete.

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arXiv2018

An accurate linear model for redshift space distortions in the void-galaxy correlation function

Redshift space distortions within voids provide a unique method to test for environmental dependence of the growth rate of structures in low density regions, where effects of modified gravity theories might be important. We derive a linear theory model for the redshift space void-galaxy correlation that is valid at all pair separations, including deep within the void, and use this to obtain expressions for the monopole $ξ^s_0$ and quadrupole $ξ^s_2$ contributions. Our derivation highlights terms that have previously been neglected but are important within the void interior. As a result our model differs from previous works and predicts new physical effects, including a change in the sign of the quadrupole term within the void radius. We show how the model can be generalised to include a velocity dispersion. We compare our model predictions to measurements of the correlation function using mock void and galaxy catalogues modelled after the BOSS CMASS galaxy sample using the Big MultiDark $N$-body simulation, and show that the linear model with dispersion provides an excellent fit to the data at all scales, $0\leq s\leq120\;h^{-1}$Mpc. While the RSD model matches simulations, the linear bias approximation does not hold within voids, and care is needed in fitting for the growth rate. We show that fits to the redshift space correlation recover the growth rate $f(z=0.52)$ to a precision of $2.7\%$ using the simulation volume of $(2.5\;h^{-1}\mathrm{Gpc})^3$.

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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.

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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.

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arXiv2018

Recent Developments in the Analysis of Galaxy Surveys

These are advanced lecture notes covering recent developments in the methodology used to analyse galaxy surveys. The focus is particularly on direct measurements of the galaxy power spectrum although I also discuss its Fourier transform, the correlation function for comparison. These 2-point statistics, under the assumption that the overdensity field has Gaussian statistics on large-scales, contain the majority of the cosmological signal available from the galaxy distribution. Recent developments in multipole measurements, dealing with systematics, convolving theoretical models with the survey window function, the approximation of covariance matrices, and weighting schemes for measuring evolution with redshift are considered. The focus is on analytic explanation of the issues involved rather than on recent analyses or simulation results.

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arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: anisotropic clustering analysis in configuration-space

We explore the cosmological implications of anisotropic clustering measurements of the quasar sample from Data Release 14 of the Sloan Digital Sky Survey IV Extended Baryon Oscillation Spectroscopic Survey (eBOSS) in configuration space. The $\sim 147,000$ quasar sample observed by eBOSS offers a direct tracer of the density field and bridges the gap of previous BAO measurements between redshift $0.8<z<2.2$. By analysing the two-point correlation function characterized by clustering wedges $ξ_{\rm w_i}(s)$ and multipoles $ξ_{\ell}(s)$, we measure the angular diameter distance, Hubble parameter and cosmic structure growth rate. We define a systematic error budget for our measurements based on the analysis of $N$-body simulations and mock catalogues. Based on the DR14 large scale structure quasar sample at the effective redshift $z_{\rm eff}=1.52$, we find the growth rate of cosmic structure $fσ_8(z_{\rm eff})=0.396\pm 0.079$, and the geometric parameters $D_{\rm V}(z)/r_{\rm d}=26.47\pm 1.23$, and $F_{\rm AP}(z)=2.53\pm 0.22$, where the uncertainties include both statistical and systematic errors. These values are in excellent agreement with the best-fitting standard ${\rm ΛCDM}$ model to the latest cosmic microwave background data from Planck.

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arXiv2018

The triply-ionized carbon forest from eBOSS: cosmological correlations with quasars in SDSS-IV DR14

We present measurements of the cross-correlation of the triply-ionized carbon (CIV) forest with quasars using Sloan Digital Sky Survey Data Release 14. The study exploits a large sample of new quasars from the first two years of observations by the Extended Baryon Oscillation Spectroscopic Survey (eBOSS). The CIV forest is a weaker tracer of large-scale structure than the Ly$α$ forest, but benefits from being accessible at redshifts $z<2$ where the quasar number density from eBOSS is high. Our data sample consists of 287,651 CIV forest quasars in the redshift range $1.4<z<3.5$ and 387,315 tracer quasars with $1.2<z<3.5$. We measure large-scale correlations from CIV absorption occuring in three distinct quasar rest-frame wavelength bands of the spectra referred to as the CIV forest, the SiIV forest and the Ly$α$ forest. From the combined fit to the quasar-CIV cross-correlations for the CIV forest and the SiIV forest, the CIV redshift-space distortion parameter is $β_{\rm CIV}=0.27_{\ -0.14}^{\ +0.16}$ and its combination with the CIV linear transmission bias parameter is $b_{\rm CIV}(1+β_{\rm CIV})=-0.0183_{\ -0.0014}^{\ +0.0013}$ ($1σ$ statistical error) at the mean redshift $z=2.00$. Splitting the sample at $z=2.2$ to constrain the bias evolution with redshift yields the power-law exponent $γ=0.60\pm0.63$, indicating a significantly weaker redshift-evolution than for the Ly$α$ forest linear transmission bias. We demonstrate that CIV absorption has the potential to be used as a probe of baryon acoustic oscillations (BAO). While the current data set is insufficient for a detection of the BAO peak feature, the final quasar samples for redshifts $1.4<z<2.2$ from eBOSS and the Dark Energy Spectroscopic Instrument (DESI) are expected to provide measurements of the isotropic BAO scale to $\sim7\%$ and $\sim3\%$ precision, respectively, at $z\simeq1.6$.

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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.

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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.

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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.

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arXiv2018

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 $fσ_8$ and parameters controlling the anisotropic projection of the cosmological perturbations. We measure $f σ_8(z=1.52)=0.43 \pm 0.05 $ and $dfσ_8/dz (z=1.52)= - 0.16 \pm 0.08$, consistent with the expectation for a $Λ$CDM cosmology as constrained by the Planck experiment.

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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.

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