We perform a tomographic baryon acoustic oscillations (BAO) analysisusing the monopole, quadrupole and hexadecapole of the redshift-spacegalaxy power spectrum measured from the pre-reconstructed combinedgalaxy sample of the completed Sloan Digital Sky Survey BaryonOscillation Spectroscopic Survey (BOSS) Data Release12 covering theredshift range of 0.20 < z < 0.75. By allowing for overlap betweenneighbouring redshift slices, we successfully obtained the isotropic andanisotropic BAO distance measurements within nine redshift slices to aprecision of 1.5-3.4 per cent for D_V/r_d, 1.8-4.2per cent for D_A/r_d and 3.7-7.5 per cent for Hr_d, depending on effective redshifts. We provide our BAOmeasurement of D_A/r_d and H r_d with thefull covariance matrix, which can be used for cosmological implications.Our measurements are consistent with those presented in Alam et al., inwhich the BAO distances are measured at three effective redshifts. Weconstrain dark energy parameters using our measurements and find animprovement of the Figure-of-Merit of dark energy in general due to thetemporal BAO information resolved. This paper is a part of a set thatanalyses the final galaxy clustering data set from BOSS.

We perform a tomographic baryon acoustic oscillations (BAOs) analysisusing the two-point galaxy correlation function measured from thecombined sample of Baryon Oscillation Spectroscopic Survey Data Release12 (BOSS DR12), which covers the redshift range of 0.2 < z < 0.75.Upon splitting the sample into multiple overlapping redshift slices toextract the redshift information of galaxy clustering, we obtain ameasurement of D_A(z)/r_d and H(z)r_d atnine effective redshifts with the full covariance matrix calibratedusing MultiDark-Patchy mock catalogues. Using the reconstructed galaxycatalogues, we obtain the precision of 1.3-2.2 per cent forD_A(z)/r_d and 2.1-6.0 per cent forH(z)r_d. To quantify the gain from the tomographicinformation, we compare the constraints on the cosmological parametersusing our nine-bin BAO measurements, the consensus three-bin BAO andredshift space distortion measurements at three effective redshifts inAlam et al., and the non-tomographic (one-bin) BAO measurement at asingle effective redshift. Comparing the nine-bin with one-binconstraint result, it can improve the dark energy Figure of Merit by afactor of 1.24 for the Chevallier-Polarski-Linder parametrization forequation-of-state parameter w_DE. The errors of w₀and w_a from nine-bin constraints are slightly improved whencompared to the three-bin constraint result.

We present a Bayesian phase-space reconstruction of the cosmiclarge-scale matter density and velocity fields from the Sloan DigitalSky Survey-III Baryon Oscillations Spectroscopic Survey Data Release 12CMASS galaxy clustering catalogue. We rely on a given Λ cold darkmatter cosmology, a mesh resolution in the range of 6-10 h^-1Mpc, and a lognormal-Poisson model with a redshift-dependent non-linearbias. The bias parameters are derived from the data and a generalrenormalized perturbation theory approach. We use combined Gibbs andHamiltonian sampling, implemented in the argo code, to iterativelyreconstruct the dark matter density field and the coherent peculiarvelocities of individual galaxies, correcting hereby for coherentredshift space distortions. Our tests relying on accurate N-body-basedmock galaxy catalogues show unbiased real space power spectra of thenon-linear density field up to k ˜ 0.2 h Mpc^-1, andvanishing quadrupoles down to r ˜ 20 h^-1 Mpc. We alsodemonstrate that the non-linear cosmic web can be obtained from thetidal field tensor based on the Gaussian component of the reconstructeddensity field. We find that the reconstructed velocities have astatistical correlation coefficient compared to the true velocities ofeach individual light-cone mock galaxy of r ˜ 0.68 including about10 per cent of satellite galaxies with virial motions (about r = 0.75without satellites). The power spectra of the velocity divergence agreewell with theoretical predictions up to k ˜ 0.2 h Mpc^-1.This work will be especially useful to improve, for example, baryonacoustic oscillation reconstructions, kinematic Sunyaev-Zeldovich,integrated Sachs-Wolfe measurements or environmental studies.

We explore the cosmological implications of anisotropic clusteringmeasurements in configuration space of the final galaxy samples fromData Release 12 of the Sloan Digital Sky Survey III Baryon OscillationSpectroscopic Survey. We implement a new detailed modelling of theeffects of non-linearities, bias and redshift-space distortions that canbe used to extract unbiased cosmological information from ourmeasurements for scales s ≳ 20 h^-1 Mpc. We combined theinformation from Baryon Oscillation Spectroscopic Survey (BOSS) with thelatest cosmic microwave background (CMB) observations and Type Iasupernovae samples and found no significant evidence for a deviationfrom the Λ cold dark matter (ΛCDM) cosmological model. Inparticular, these data sets can constrain the dark energyequation-of-state parameter to w_DE = -0.996 ± 0.042when to be assumed time independent, the curvature of the Universe toΩ_k = -0.0007 ± 0.0030 and the sum of theneutrino masses to ∑m_ν < 0.25 eV at 95 per centconfidence levels. We explore the constraints on the growth rate ofcosmic structures assuming f(z) =Ω_m(z)^γ and obtain γ = 0.609± 0.079, in good agreement with the predictions of generalrelativity of γ = 0.55. We compress the information of ourclustering measurements into constraints on the parameter combinationsD_V(z)/r_d, F_AP(z) andfσ₈(z) at z_eff = 0.38, 0.51 and 0.61 withtheir respective covariance matrices and find good agreement with thepredictions for these parameters obtained from the best-fittingΛCDM model to the CMB data from the Planck satellite. This paperis part of a set that analyses the final galaxy clustering data set fromBOSS. The measurements and likelihoods presented here are combined withothers by Alam et al. to produce the final cosmological constraints fromBOSS.

We investigate the anisotropic clustering of the Baryon OscillationSpectroscopic Survey (BOSS) Data Release 12 sample, which consists of1198 006 galaxies in the redshift range 0.2 < z < 0.75 and a skycoverage of 10 252 deg². We analyse this data set in Fourierspace, using the power-spectrum multipoles to measure redshift-spacedistortions simultaneously with the Alcock-Paczynski effect and thebaryon acoustic oscillation scale. We include the power-spectrummonopole, quadrupole and hexadecapole in our analysis and compare ourmeasurements with a perturbation-theory-based model, while properlyaccounting for the survey window function. To evaluate the reliabilityof our analysis pipeline, we participate in a mock challenge, whichresults in systematic uncertainties significantly smaller than thestatistical uncertainties. While the high-redshift constraint onfσ₈ at z_eff = 0.61 indicates a small(˜1.4σ) deviation from the prediction of the PlanckΛCDM (Λ cold dark matter) model, the low-redshiftconstraint is in good agreement with Planck ΛCDM. This paper ispart of a set that analyses the final galaxy clustering data set fromBOSS. The measurements and likelihoods presented here are combined withothers in Alam et al. to produce the final cosmological constraints fromBOSS.

We analyse the baryon acoustic oscillation (BAO) signal of the finalBaryon Oscillation Spectroscopic Survey (BOSS) data release (DR12). Ouranalysis is performed in the Fourier space, using the power spectrummonopole and quadrupole. The data set includes 1198 006 galaxies overthe redshift range 0.2 < z < 0.75. We divide this data set intothree (overlapping) redshift bins with the effective redshiftsz_eff = 0.38, 0.51 and 0.61. We demonstrate the reliability ofour analysis pipeline using N-body simulations as well as ˜1000MultiDark-Patchy mock catalogues that mimic the BOSS-DR12 targetselection. We apply density field reconstruction to enhance the BAOsignal-to-noise ratio. By including the power spectrum quadrupole we canseparate the line of sight and angular modes, which allows us toconstrain the angular diameter distance D_A(z) and the Hubbleparameter H(z) separately. We obtain two independent 1.6 and 1.5 percent constraints on D_A(z) and 2.9 and 2.3 per centconstraints on H(z) for the low (z_eff = 0.38) and high(z_eff = 0.61) redshift bin, respectively. We obtain twoindependent 1 and 0.9 per cent constraints on the angular averageddistance D_V(z), when ignoring the Alcock-Paczynski effect.The detection significance of the BAO signal is of the order of 8σ(post-reconstruction) for each of the three redshift bins. Our resultsare in good agreement with the Planck prediction within Λ colddark matter. This paper is part of a set that analyses the final galaxyclustering data set from BOSS. The measurements and likelihoodspresented here are combined with others in Alam et al. to produce thefinal cosmological constraints from BOSS.

We present a measurement of the linear growth rate of structure, f, fromthe Sloan Digital Sky Survey III (SDSS-III) Baryon OscillationSpectroscopic Survey (BOSS) Data Release 12 (DR12) using convolutionLagrangian perturbation theory (CLPT) with Gaussian streaming redshiftspace distortions (GSRSD) to model the two-point statistics of BOSSgalaxies in DR12. The BOSS-DR12 data set includes 1198 006 massivegalaxies spread over the redshift range 0.2 < z < 0.75. Thesegalaxy samples are categorized in three redshift bins. Using CLPT-GSRSDin our analysis of the combined sample of the three redshift bins, wereport measurements of fσ₈ for the three redshift bins.We find fσ₈ = 0.430 ± 0.054 at z_eff =0.38, fσ₈ = 0.452 ± 0.057 at z_eff =0.51 and fσ₈ = 0.457 ± 0.052 at z_eff= 0.61. Our results are consistent with the predictions of PlanckΛ cold dark matter-general relativity. Our constraints on thegrowth rates of structure in the Universe at different redshifts serveas a useful probe, which can help distinguish between a model of theUniverse based on dark energy and models based on modified theories ofgravity. This paper is part of a set that analyses the final galaxyclustering data set from BOSS. The measurements and likelihoodspresented here are combined with others in Alam et al., to produce thefinal cosmological constraints from BOSS.

We extract cosmological information from the anisotropic power-spectrummeasurements from the recently completed Baryon OscillationSpectroscopic Survey (BOSS), extending the concept of clustering wedgesto Fourier space. Making use of new fast-Fourier-transform-basedestimators, we measure the power-spectrum clustering wedges of the BOSSsample by filtering out the information of Legendre multipoles ℓ> 4. Our modelling of these measurements is based on novel approachesto describe non-linear evolution, bias and redshift-space distortions,which we test using synthetic catalogues based on large-volume N-bodysimulations. We are able to include smaller scales than in previousanalyses, resulting in tighter cosmological constraints. Using threeoverlapping redshift bins, we measure the angular-diameter distance, theHubble parameter and the cosmic growth rate, and explore thecosmological implications of our full-shape clustering measurements incombination with cosmic microwave background and Type Ia supernova data.Assuming a Λ cold dark matter (ΛCDM) cosmology, weconstrain the matter density to Ω _M=0.311_{-0.010}^{+0.009} and the Hubble parameter to H_0 =67.6_{-0.6}^{+0.7} km s^{-1 Mpc^{-1}}, at a confidence level of 68 percent. We also allow for non-standard dark energy models andmodifications of the growth rate, finding good agreement with theΛCDM paradigm. For example, we constrain the equation-of-stateparameter to w = -1.019_{-0.039}^{+0.048}. This paper is part of a setthat analyses the final galaxy-clustering data set from BOSS. Themeasurements and likelihoods presented here are combined with others inAlam et al. to produce the final cosmological constraints from BOSS.

We present baryon acoustic oscillation (BAO) scale measurementsdetermined from the clustering of 1.2 million massive galaxies withredshifts 0.2 < z < 0.75 distributed over 9300 deg², asquantified by their redshift-space correlation function. In order tofacilitate these measurements, we define, describe, and motivate theselection function for galaxies in the final data release (DR12) of theSDSS III Baryon Oscillation Spectroscopic Survey (BOSS). This includesthe observational footprint, masks for image quality and Galacticextinction, and weights to account for density relationships intrinsicto the imaging and spectroscopic portions of the survey. We simulate theobserved systematic trends in mock galaxy samples and demonstrate thatthey impart no bias on BAO scale measurements and have a minor impact onthe recovered statistical uncertainty. We measure transverse and radialBAO distance measurements in 0.2 < z < 0.5, 0.5 < z < 0.75,and (overlapping) 0.4 < z < 0.6 redshift bins. In each redshiftbin, we obtain a precision that is 2.7 per cent or better on the radialdistance and 1.6 per cent or better on the transverse distance. Thecombination of the redshift bins represents 1.8 per cent precision onthe radial distance and 1.1 per cent precision on the transversedistance. This paper is part of a set that analyses the final galaxyclustering data set from BOSS. The measurements and likelihoodspresented here are combined with others in Alam et al. to produce thefinal cosmological constraints from BOSS.

We develop a new computationally efficient methodology calleddouble-probe analysis with the aim of minimizing informative priors(those coming from extra probes) in the estimation of cosmologicalparameters. Using our new methodology, we extract the dark energymodel-independent cosmological constraints from the joint data sets ofthe Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample andPlanck cosmic microwave background (CMB) measurements. We measure themean values and covariance matrix of {R, l_a,Ω_bh², n_s, log(A_s),Ω_k, H(z), D_A(z),f(z)σ₈(z)}, which give an efficient summary of thePlanck data and two-point statistics from the BOSS galaxy sample. TheCMB shift parameters are R=√{Ω _m H_0^2} r(z_*) andl_a = πr(z_*)/r_s(z_*), wherez_* is the redshift at the last scattering surface, andr(z_*) and r_s(z_*) denote our comovingdistance to the z_* and sound horizon at z_*,respectively; Ω_b is the baryon fraction at z = 0. Thisapproximate methodology guarantees that we will not need to putinformative priors on the cosmological parameters that galaxy clusteringis unable to constrain, I.e. Ω_bh² andn_s. The main advantage is that the computational timerequired for extracting these parameters is decreased by a factor of 60with respect to exact full-likelihood analyses. The results obtainedshow no tension with the flat Λ cold dark matter (ΛCDM)cosmological paradigm. By comparing with the full-likelihood exactanalysis with fixed dark energy models, on one hand we demonstrate thatthe double-probe method provides robust cosmological parameterconstraints that can be conveniently used to study dark energy models,and on the other hand we provide a reliable set of measurements assumingdark energy models to be used, for example, in distance estimations. Weextend our study to measure the sum of the neutrino mass using differentmethodologies, including double-probe analysis (introduced in thisstudy), full-likelihood analysis and single-probe analysis. Fromfull-likelihood analysis, we obtain Σm_ν < 0.12(68 per cent), assuming ΛCDM and Σm_ν <0.20 (68 per cent) assuming owCDM. We also find that there is degeneracybetween observational systematics and neutrino masses, which suggeststhat one should take great care when estimating these parameters in thecase of not having control over the systematics of a given sample.

The cosmological information contained in anisotropic galaxy clusteringmeasurements can often be compressed into a small number of parameterswhose posterior distribution is well described by a Gaussian. We presenta general methodology to combine these estimates into a single set ofconsensus constraints that encode the total information of theindividual measurements, taking into account the full covariance betweenthe different methods. We illustrate this technique by applying it tocombine the results obtained from different clustering analyses,including measurements of the signature of baryon acoustic oscillationsand redshift-space distortions, based on a set of mock catalogues of thefinal SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS). Ourresults show that the region of the parameter space allowed by theconsensus constraints is smaller than that of the individual methods,highlighting the importance of performing multiple analyses on galaxysurveys even when the measurements are highly correlated. This paper ispart of a set that analyses the final galaxy clustering data set fromBOSS. The methodology presented here is used in Alam et al. to producethe final cosmological constraints from BOSS.

We probe the higher order clustering of the galaxies in the final datarelease (DR12) of the Sloan Digital Sky Survey Baryon OscillationSpectroscopic Survey (BOSS), using the method of germ-grain Minkowskifunctionals (MFs). Our sample consists of 410 615 BOSS galaxies from thenorthern Galactic cap in the redshift range 0.450-0.595. We show the MFsto be sensitive to contributions up to the six-point correlationfunction for this data set. We ensure with a custom angular mask thatthe results are more independent of boundary effects than in previousanalyses of this type. We extract the higher order part of the MFs andquantify the difference to the case without higher order correlations.The resulting χ² value of over 10 000 for a modest numberof degrees of freedom, O(200), indicates a 100σ deviation anddemonstrates that we have a highly significant signal of thenon-Gaussian contributions to the galaxy distribution. This statisticalpower can be useful in testing models with differing higher ordercorrelations. Comparing the galaxy data to the quick particle mesh andMultiDark(MD)-Patchy mocks, we find that the latter better describes theobserved structure. From an order-by-order decomposition, we expectthat, for example, already a reduction of the amplitude of the MD-Patchymock power spectrum by 5 per cent would remove the remaining tension.

We measure the color and stellar mass dependence of clustering inspectroscopic galaxies at 0.6 < z < 0.65 using data from theBaryon Oscillation Spectroscopic Survey component of the Sloan DigitalSky Survey. We greatly increase the statistical precision of ourclustering measurements by using the cross-correlation of 66,657spectroscopic galaxies to a sample of 6.6 million fainter photometricgalaxies. The clustering amplitude w(R) is measured as the ratio of themean excess number of photometric galaxies found within a specifiedradius annulus around a spectroscopic galaxy to that from a randomphotometric galaxy distribution. We recover many of the familiar trendsat high signal-to-noise ratio. We find the ratio of the clusteringamplitudes of red and blue massive galaxies to be{w}_{red}/{w}_{blue}=1.92+/- 0.11 in our smallestannulus of 75-125 kpc. At our largest radii (2-4 Mpc), wefind {w}_{red}/{w}_{blue}=1.24+/- 0.05. Red galaxiestherefore have denser environments than their blue counterparts at z˜ 0.625, and this effect increases with decreasing radius.Irrespective of color, we find that w(R) does not obey a simplepower-law relation with radius, showing a dip around 1 Mpc. Holdingstellar mass fixed, we find a clear differentiation between clusteringin red and blue galaxies, showing that clustering is not solelydetermined by stellar mass. Holding color fixed, we find that clusteringincreases with stellar mass, especially for red galaxies at small scales(more than a factor of 2 effect over 0.75 dex in stellar mass).

We propose a method to substantially increase the flexibility and powerof template fitting-based photometric redshifts by transforming a largenumber of galaxy spectral templates into a corresponding collection of'fuzzy archetypes' using a suitable set of perturbative priors designedto account for empirical variation in dust attenuation and emission-linestrengths. To bypass widely separated degeneracies in parameter space(e.g. the redshift-reddening degeneracy), we train self-organizing maps(SOMs) on large 'model catalogues' generated from Monte Carlo samplingof our fuzzy archetypes to cluster the predicted observables in atopologically smooth fashion. Subsequent sampling over the SOM thenallows full reconstruction of the relevant probability distributionfunctions (PDFs). This combined approach enables the multimodalexploration of known variation among galaxy spectral energydistributions with minimal modelling assumptions. We demonstrate thepower of this approach to recover full redshift PDFs using discreteMarkov chain Monte Carlo sampling methods combined with SOMs constructedfrom Large Synoptic Survey Telescope ugrizY and Euclid YJH mockphotometry.

With an eye towards the computational requirements of future large-scalesurveys such as Euclid and Large Synoptic Survey Telescope (LSST) thatwill require photometric redshifts (photo-z's) for ≳ 10⁹objects, we investigate a variety of ways that 'fuzzy archetypes' can beused to improve photometric redshifts and explore their respectivestatistical interpretations. We characterize their relative performanceusing an idealized LSST ugrizY and Euclid YJH mock catalogue of 10 000objects spanning z = 0-6 at Y = 24 mag. We find most schemes are able torobustly identify redshift probability distribution functions that aremultimodal and/or poorly constrained. Once these objects are flagged andremoved, the results are generally in good agreement with the strictaccuracy requirements necessary to meet Euclid weak lensing goals formost redshifts between 0.8 ≲ z ≲ 2. These results demonstratethe statistical robustness and flexibility that can be gained bycombining template-fitting and machine-learning methods and provideuseful insights into how astronomers can further exploit thecolour-redshift relation.

We present the large-scale three-point correlation function (3PCF) ofthe Sloan Digital Sky Survey DR12 Constant stellar Mass (CMASS) sampleof 777 202 Luminous Red Galaxies, the largest-ever sample used for a3PCF or bispectrum measurement. We make the first high-significance(4.5σ) detection of baryon acoustic oscillations (BAO) in the3PCF. Using these acoustic features in the 3PCF as a standard ruler, wemeasure the distance to z = 0.57 to 1.7 per cent precision (statisticalplus systematic). We find D_V = 2024 ± 29 Mpc (stat)± 20 Mpc (sys) for our fiducial cosmology (consistent with Planck2015) and bias model. This measurement extends the use of the BAOtechnique from the two-point correlation function (2PCF) and powerspectrum to the 3PCF and opens an avenue for deriving additionalcosmological distance information from future large-scale structureredshift surveys such as DESI. Our measured distance scale from the 3PCFis fairly independent from that derived from the pre-reconstruction 2PCFand is equivalent to increasing the length of BOSS by roughly 10 percent; reconstruction appears to lower the independence of the distancemeasurements. Fitting a model including tidal tensor bias yields amoderate-significance (2.6σ) detection of this bias with a valuein agreement with the prediction from local Lagrangian biasing.

We report a measurement of the large-scale three-point correlationfunction of galaxies using the largest data set for this purpose todate, 777 202 luminous red galaxies in the Sloan Digital Sky SurveyBaryon Acoustic Oscillation Spectroscopic Survey (SDSS BOSS) DR12 CMASSsample. This work exploits the novel algorithm of Slepian &Eisenstein to compute the multipole moments of the 3PCF in O(N^2) time,with N the number of galaxies. Leading-order perturbation theory modelsthe data well in a compressed basis where one triangle side isintegrated out. We also present an accurate and computationallyefficient means of estimating the covariance matrix. With thesetechniques, the redshift-space linear and non-linear bias are measured,with 2.6 per cent precision on the former if σ₈ isfixed. The data also indicate a 2.8σ preference for the BAO,confirming the presence of BAO in the three-point function.

We have used flux-transmission correlations in Lyα forests tomeasure the imprint of baryon acoustic oscillations (BAO). The studyuses spectra of 157 783 quasars in the redshift range 2.1 ≤ z ≤3.5 from the Sloan Digital Sky Survey (SDSS) data release 12 (DR12).Besides the statistical improvements on our previous studies using SDSSDR9 and DR11, we have implemented numerous improvements in the analysisprocedure, allowing us to construct a physical model of the correlationfunction and to investigate potential systematic errors in thedetermination of the BAO peak position. The Hubble distance,D_H = c/H(z), relative to the sound horizon is D_H(z= 2.33) /r_d = 9.07 ± 0.31. The best-determinedcombination of comoving angular-diameter distance, D_M, andthe Hubble distance is found to beD_H^0.7D_M^0.3 /r_d =13.94 ± 0.35. This value is 1.028 ± 0.026 times theprediction of the flat-ΛCDM model consistent with the cosmicmicrowave background (CMB) anisotropy spectrum. The errors includemarginalization over the effects of unidentified high-density absorptionsystems and fluctuations in ultraviolet ionizing radiation.Independently of the CMB measurements, the combination of our resultsand other BAO observations determine the open-ΛCDM densityparameters to be Ω_M = 0.296 ± 0.029,Ω_Λ = 0.699 ± 0.100 andΩ_k = -0.002 ± 0.119.

We present a configuration-space model of the large-scale galaxy 3-pointcorrelation function (3PCF) based on leading-order perturbation theoryand including redshift-space distortions (RSD). This model should beuseful in extracting distance-scale information from the 3PCF via thebaryon acoustic oscillation method. We include the first redshift-spacetreatment of biasing by the baryon-dark matter relative velocity.Overall, on large scales the effect of RSD is primarily arenormalization of the 3PCF that is roughly independent of both physicalscale and triangle opening angle; for our adopted Ω_mand bias values, the rescaling is a factor of ˜1.8. We also presentan efficient scheme for computing 3PCF predictions from our model,important for allowing fast exploration of the space of cosmologicalparameters in future analyses.

We test for galactic conformity at 0.2< z< 1.0 to a projecteddistance of 5 Mpc using spectroscopic redshifts from the PRismMUlti-object Survey (PRIMUS). Our sample consists of ˜60,000galaxies in five separate fields covering a total of ˜5.5 squaredegrees, which allows us to account for cosmic variance. We identifystar-forming and quiescent “isolated primary” (I.e.,central) galaxies using isolation criteria and cuts in specific starformation rate. We match the redshift and stellar mass distributions ofthese samples to control for correlations between quiescent fraction andredshift and stellar mass. We detect a significant (>3σ)one-halo conformity signal, or an excess of star-forming neighbors