arXiv subjects

Hélion du Mas des Bourboux

Publications and source records attributed to Hélion du Mas des Bourboux.

36 records · Page 2Linked to original sources

arXiv2020

Removing Imaging Systematics from Galaxy Clustering Measurements with Obiwan : Application to the SDSS-IV extended Baryon Oscillation Spectroscopic Survey Emission Line Galaxy Sample

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 3-dimensional (3D) clustering statistics. This is a forward model of the process by which images of the night sky are transformed into a 3D large--scale structure catalog. The photometric pipeline automatically detects and models galaxies and then generates a catalog 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 catalogs 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 extend Baryon Oscillation Spectroscopic Survey Emission Line Galaxies (ELG) sample. 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 full eBOSS sample. We find the results are consistent, thereby validating the eBOSS ELG catalogs, presented in Raichoor(2020), used to obtain cosmological results.

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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 $z_{\rm eff}=0.845$.

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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.

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arXiv2019

The one-dimensional power spectrum from the SDSS DR14 Ly$α$ forests

We present a measurement of the 1D Ly$α$ forest flux power spectrum, using the complete Baryon Oscillation Spectroscopic Survey (BOSS) and first extended-BOSS (eBOSS) quasars at $z_{\rm qso}>2.1$, corresponding to the fourteenth data release (DR14) of the Sloan Digital Sky Survey (SDSS). Our results cover thirteen bins in redshift from $z_{\rm Lyα}=2.2$ to 4.6, and scales up to $k=0.02\rm \,(km/s)^{-1}$. From a parent sample of 180,413 visually inspected spectra, we selected the 43,751 quasars with the best quality; this data set improves the previous result from the ninth data release (DR9), both in statistical precision (achieving a reduction by a factor of two) and in redshift coverage. We also present a thorough investigation of identified sources of systematic uncertainties that affect the measurement. The resulting 1D power spectrum of this work is in excellent agreement with the one from the BOSS DR9 data.

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arXiv2019

Baryon acoustic oscillations at z = 2.34 from the correlations of Ly$α$ absorption in eBOSS DR14

We measure the imprint of primordial baryon acoustic oscillations (BAO) in the correlation function of Ly$α$ absorption in quasar spectra from the Baryon Oscillation Spectroscopic Survey (BOSS) and the extended BOSS (eBOSS) in Data Release 14 (DR14) of the Sloan Digital Sky Survey (SDSS)-IV. In addition to 179,965 spectra with absorption in the Lyman-$α$ (Ly$α$) region, we use, for the first time, Ly$α$ absorption in the Lyman-$β$ region of 56,154 spectra. We measure the Hubble distance, $D_H$, and the comoving angular diameter distance, $D_M$, relative to the sound horizon at the drag epoch $r_d$ at an effective redshift $z=2.34$. Using a physical model of the correlation function outside the BAO peak, we find $D_H(2.34)/r_d=8.86\pm 0.29$ and $D_M(2.34)/r_d=37.41\pm 1.86$, within 1$σ$ from the flat-$Λ$CDM model consistent with CMB anisotropy measurements. With the addition of polynomial "broadband" terms, the results remain within one standard deviation of the CMB-inspired model. Combined with the quasar-Ly$α$ cross-correlation measurement presented in a companion paper Blomqvist19, the BAO measurements at $z=2.35$ are within 1.7$σ$ of the predictions of this model.

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arXiv2019

Baryon acoustic oscillations from the cross-correlation of Ly$α$ absorption and quasars in eBOSS DR14

We present a measurement of the baryon acoustic oscillation (BAO) scale at redshift $z=2.35$ from the three-dimensional correlation of Lyman-$α$ (Ly$α$) forest absorption and quasars. The study uses 266,590 quasars in the redshift range $1.77<z<3.5$ from the Sloan Digital Sky Survey (SDSS) Data Release 14 (DR14). The sample includes the first two years of observations by the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS), providing new quasars and re-observations of BOSS quasars for improved statistical precision. Statistics are further improved by including Ly$α$ absorption occurring in the Ly$β$ wavelength band of the spectra. From the measured BAO peak position along and across the line of sight, we determined the Hubble distance $D_{H}$ and the comoving angular diameter distance $D_{M}$ relative to the sound horizon at the drag epoch $r_{d}$: $D_{H}(z=2.35)/r_{d}=9.20\pm 0.36$ and $D_{M}(z=2.35)/r_{d}=36.3\pm 1.8$. These results are consistent at $1.5σ$ with the prediction of the best-fit spatially-flat cosmological model with the cosmological constant reported for the Planck (2016) analysis of cosmic microwave background anisotropies. Combined with the Ly$α$ auto-correlation measurement presented in a companion paper, the BAO measurements at $z=2.34$ are within $1.7σ$ of the predictions of this model.

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arXiv2019

The extended Baryon Oscillation Spectroscopic Survey: measuring the cross-correlation between the MgII flux transmission field and quasars and galaxies at $z=0.59$

We present the first attempt at measuring the baryonic acoustic oscillations (BAO) in the large scale cross-correlation between the magnesium-II doublet (MgII) flux transmission field and the position of quasar and galaxy tracers. The MgII flux transmission continuous field at $0.3 < z < 1.6$ is measured from 500,589 quasar spectra obtained in the Baryonic Oscillation Spectroscopic Survey (BOSS) and the extended BOSS (eBOSS). The position of 246,697 quasar tracers and 1,346,776 galaxy tracers are extracted from the Sloan Digital Sky Survey (SDSS) I, II, BOSS and eBOSS catalogs. In addition to measuring the cosmological BAO scale and the biased matter density correlation, this study allows tests and improvements to cosmological Lyman-$α$ analyses. A feature consistent with that of the BAO is detected at a significance of $Δχ^{2} = 7.25$. The measured MgII linear transmission bias parameters are $b_{\mathrm{MgII(2796)}} (z = 0.59) = (-6.82 \pm 0.54) \, \times 10^{-4}$ and $b_{\mathrm{MgII(2804)}} (z = 0.59) = (-5.55 \pm 0.46) \, \times 10^{-4}$, and the MgI bias is $b_{\mathrm{MgI(2853)}} (z = 0.59) = (-1.48 \pm 0.24) \, \times 10^{-4}$. Their redshift evolution is characterized by the power-law index: $γ_{\mathrm{Mg}} = 3.36 \pm 0.46$. These measurements open a new window towards using BAO from flux transmission at $z < 1$ in the final eBOSS sample and in the upcoming sample from the Dark Energy Spectroscopic Instrument.

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arXiv2019

Measurements of effective optical depth in the Ly$α$ forest from the BOSS DR12 Quasar sample

We measure the effective optical depth in the Lyman-alpha (Ly$α$) forest using 40,035 quasar spectra from the Twelfth Data Release (DR12) of the Baryon Oscillation Spectroscopic Survey (BOSS) of SDSS-IV. A rigorous selection based on spectral index and the equivalent width of the C IV emission line is applied to choose seven uniform samples with minimal intrinsic variations across redshifts. Modeling the redshift evolution of the effective optical depth with a power-law, $τ_\mathrm{eff}=τ_0 (1 + z)^γ$ produces $τ_0=(5.54 \pm 0.64)\times 10^{-3}$ and $γ=3.182 \pm 0.074$. The 2.2% precision estimate on $γ$ is dominated by systematic errors, likely arising from the bias and uncertainties in spectral index estimates. Even after incorporating the systematic errors, this work provides the most precise estimates of optical depth parameters to date. Finally, using the reconstructed Ly$α$ forest continuum to directly measure the transmitted flux ratio as a function of redshift, we find deviations of less than 2.5% from the predictions from the global model and no convincing evidence for signal associated with He II reionization.

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arXiv2018

The Spectroscopic Signature of Variability in High-Redshift Quasars

Using 16,421 spectra from a sample of 340 quasars ($1.62<z<3.30$) from the SDSS Reverberation Mapping Project, we present an analysis of quasar spectral variability. We confirm the intrinsic Baldwin Effect and brighter-means-bluer trends in which emission line strength and color are associated with changes in luminosity. We then create a composite differential spectrum that captures the wavelength dependence of quasar variability as a function of change in luminosity. When using a bandpass around 1740 Å to describe the luminosity, the differential spectrum follows a power law at longer wavelengths that breaks blueward of 1700 Å. However, the shape of the differential spectrum, the location of the power law break, and the slope of the intrinsic Baldwin Effect all vary with the choice of bandpass used to define the change in quasar luminosity. We propose that the observed behavior can be explained by inhomogeneous accretion or slim accretion disk models where delays in the reprocessing of incident light on the accretion disk cause local deviations in temperature from the thin disk model. Finally, we quantify the effects on cosmology studies due to the variations in the quasar spectrum in the Lyman-$α$ forest wavelength range. Using the observed spectroscopic signatures to predict the quasar continuum over the interval $1040 < λ< 1200$ Å, we find that the derived spectral templates can reduce the uncertainty of the Lyman-$α$ forest continuum level in individual epochs from 17.2% to 7.7%, near the level where systematic errors in SDSS flux calibration are expected to dominate.

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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

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.

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arXiv2017

Baryon acoustic oscillations from the complete SDSS-III Ly$α$-quasar cross-correlation function at $z=2.4$

We present a measurement of baryon acoustic oscillations (BAO) in the cross-correlation of quasars with the Ly$α$-forest flux-transmission at a mean redshift $z=2.40$. The measurement uses the complete SDSS-III data sample: 168,889 forests and 234,367 quasars from the SDSS Data Release DR12. In addition to the statistical improvement on our previous study using DR11, we have implemented numerous improvements at the analysis level allowing a more accurate measurement of this cross-correlation. We also developed the first simulations of the cross-correlation allowing us to test different aspects of our data analysis and to search for potential systematic errors in the determination of the BAO peak position. We measure the two ratios $D_{H}(z=2.40)/r_{d} = 9.01 \pm 0.36$ and $D_{M}(z=2.40)/r_{d} = 35.7 \pm 1.7$, where the errors include marginalization over the non-linear velocity of quasars and the metal - quasar cross-correlation contribution, among other effects. These results are within $1.8σ$ of the prediction of the flat-$Λ$CDM model describing the observed CMB anisotropies. We combine this study with the Ly$α$-forest auto-correlation function [2017A&A...603A..12B], yielding $D_{H}(z=2.40)/r_{d} = 8.94 \pm 0.22$ and $D_{M}(z=2.40)/r_{d} = 36.6 \pm 1.2$, within $2.3σ$ of the same flat-$Λ$CDM model.

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arXiv2017

The SDSS-DR12 large-scale cross-correlation of Damped Lyman Alpha Systems with the Lyman Alpha Forest

We present a measurement of the DLA mean bias from the cross-correlation of DLA and the Ly$α$ forest, updating earlier results of Font-Ribera et al. 2012 with the final BOSS Data Release and an improved method to address continuum fitting corrections. Our cross-correlation is well fitted by linear theory with the standard $ΛCDM$ model, with a DLA bias of $b_{\rm DLA} = 1.99\pm 0.11$; a more conservative analysis, which removes DLA in the Ly$β$ forest and uses only the cross-correlation at $r> 10{\rm h^{-1}\,Mpc}$, yields $b_{\rm DLA} = 2.00\pm 0.19$. This assumes the cosmological model from \cite{Planck2015} and the Ly$α$ forest bias factors of Bautista et al. 2017, and includes only statistical errors obtained from bootstrap analysis. The main systematic errors arise from possible impurities and selection effects in the DLA catalogue, and from uncertainties in the determination of the Ly$α$ forest bias factors and a correction for effects of high column density absorbers. We find no dependence of the DLA bias on column density or redshift. The measured bias value corresponds to a host halo mass $\sim 4\cdot10^{11} {\rm M_{\odot}}$ if all DLA were hosted in halos of a similar mass. In a realistic model where host halos over a broad mass range have a DLA cross section $Σ(M_h) \propto M_h^α$ down to $M_h > M_{\rm min} =10^{8.5} {\rm M_{\odot}}$, we find that $α> 1$ is required to have $b_{\rm DLA}> 1.7$, implying a steeper relation or higher value of $M_{\rm min}$ than is generally predicted in numerical simulations of galaxy formation.

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arXiv2017

Sloan Digital Sky Survey IV: Mapping the Milky Way, Nearby Galaxies, and the Distant Universe

We describe the Sloan Digital Sky Survey IV (SDSS-IV), a project encompassing three major spectroscopic programs. The Apache Point Observatory Galactic Evolution Experiment 2 (APOGEE-2) is observing hundreds of thousands of Milky Way stars at high resolution and high signal-to-noise ratio in the near-infrared. The Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey is obtaining spatially-resolved spectroscopy for thousands of nearby galaxies (median redshift of z = 0.03). The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is mapping the galaxy, quasar, and neutral gas distributions between redshifts z = 0.6 and 3.5 to constrain cosmology using baryon acoustic oscillations, redshift space distortions, and the shape of the power spectrum. Within eBOSS, we are conducting two major subprograms: the SPectroscopic IDentification of eROSITA Sources (SPIDERS), investigating X-ray AGN and galaxies in X-ray clusters, and the Time Domain Spectroscopic Survey (TDSS), obtaining spectra of variable sources. All programs use the 2.5-meter Sloan Foundation Telescope at Apache Point Observatory; observations there began in Summer 2014. APOGEE-2 also operates a second near-infrared spectrograph at the 2.5-meter du Pont Telescope at Las Campanas Observatory, with observations beginning in early 2017. Observations at both facilities are scheduled to continue through 2020. In keeping with previous SDSS policy, SDSS-IV provides regularly scheduled public data releases; the first one, Data Release 13, was made available in July 2016.

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arXiv2017

Exploring cosmic homogeneity with the BOSS DR12 galaxy sample

In this study, we probe the transition to cosmic homogeneity in the Large Scale Structure (LSS) of the Universe using the CMASS galaxy sample of BOSS spectroscopic survey which covers the largest effective volume to date, $3\ h^{-3}\ \mathrm{Gpc}^3$ at $0.43 \leq z \leq 0.7$. We study the scaled counts-in-spheres, $\mathcal{N}( 2.97$ for $r>\mathcal{R}_H$, we find $\mathcal{R}_H = (63.3\pm0.7) \ h^{-1}\ \mathrm{Mpc}$, in agreement at the percentage level with the predictions of the $Λ$CDM model $\mathcal{R}_H=62.0\ h^{-1}\ \mathrm{Mpc}$. Thanks to the large cosmic depth of the survey, we investigate the redshift evolution of the transition to homogeneity scale and find agreement with the $Λ$CDM prediction. Finally, we find that $\mathcal{D}_2$ is compatible with $3$ at scales larger than $300\ h^{-1}\ $Mpc in all redshift bins. These results consolidate the Cosmological Principle and represent a precise consistency test of the $ΛCDM$ model.

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arXiv2017

Clustering of quasars in SDSS-IV eBOSS : study of potential systematics and bias determination

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, $b_Q = 2.45 \pm 0.05$ at $\bar z=1.55$, 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 $\sim$500,000 eBOSS quasar sample.

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arXiv2017

Measurement of BAO correlations at $z=2.3$ with SDSS DR12 \lya-Forests

We use flux-transmission correlations in \Lya forests to measure the imprint of baryon acoustic oscillations (BAO). The study uses spectra of 157,783 quasars in the redshift range $2.1\le z \le 3.5$ from the Sloan Digital Sky Survey (SDSS) Data Release 12 (DR12). Besides the statistical improvements on our previous studies using SDSS DR9 and DR11, we have implemented numerous improvements in the analysis procedure, allowing us to construct a physical model of the correlation function and to investigate potential systematic errors in the determination of the BAO peak position. The Hubble distance, $\DHub=c/H(z)$, relative to the sound horizon is $\DHub(z=2.33)/r_d=9.07 \pm 0.31$. The best-determined combination of comoving angular-diameter distance, $\DM$, and the Hubble distance is found to be $\DHub^{0.7}\DM^{0.3}/r_d=13.94\pm0.35$. This value is $1.028\pm0.026$ times the prediction of the flat-\lcdm model consistent with the cosmic microwave background (CMB) anisotropy spectrum. The errors include marginalization over the effects of unidentified high-density absorption systems and fluctuations in ultraviolet ionizing radiation. Independently of the CMB measurements, the combination of our results and other BAO observations determine the open-\lcdm density parameters to be $\om=0.296 \pm 0.029$, $\ol=0.699 \pm 0.100$ and $Ω_k = -0.002 \pm 0.119$.

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arXiv2016

A 14 $h^{-3}$ Gpc$^3$ study of cosmic homogeneity using BOSS DR12 quasar sample

The BOSS quasar sample is used to study cosmic homogeneity with a 3D survey in the redshift range $2.2<z<2.8$. We measure the count-in-sphere, $N(<\! r)$, i.e. the average number of objects around a given object, and its logarithmic derivative, the fractal correlation dimension, $D_2(r)$. For a homogeneous distribution $N(<\! r) \propto r^3$ and $D_2(r)=3$. Due to the uncertainty on tracer density evolution, 3D surveys can only probe homogeneity up to a redshift dependence, i.e. they probe so-called "spatial isotropy". Our data demonstrate spatial isotropy of the quasar distribution in the redshift range $2.2<z<2.8$ in a model-independent way, independent of any FLRW fiducial cosmology, resulting in $3-\langle D_2 \rangle < 1.7 \times 10^{-3}$ (2 $σ$) over the range $250<r<1200 \, h^{-1}$Mpc for the quasar distribution. If we assume that quasars do not have a bias much less than unity, this implies spatial isotropy of the matter distribution on large scales. Then, combining with the Copernican principle, we finally get homogeneity of the matter distribution on large scales. Alternatively, using a flat $Λ$CDM fiducial cosmology with CMB-derived parameters, and measuring the quasar bias relative to this $Λ$CDM model, our data provide a consistency check of the model, in terms of how homogeneous the Universe is on different scales. $D_2(r)$ is found to be compatible with our $Λ$CDM model on the whole $10<r<1200 \, h^{-1}$Mpc range. For the matter distribution we obtain $3-\langle D_2 \rangle < 5 \times 10^{-5}$ (2 $σ$) over the range $250<r<1200 \, h^{-1}$Mpc, consistent with homogeneity on large scales.

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