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Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability of forming galaxy in a region with a given density field -- is usually approximated through a parametric expansion, we show here, that it can also be measured directly from simulations in a non-parameteric way. Our measurements show that the Lagrangian bias function is very close to a Gaussian for halo selections of any mass. Therefore, we newly introduce a Gaussian bias model with several intriguing properties: (1) It predicts only strictly positive probabilities $f > 0$ (unlike expansion models), (2) It has a simple analytic renormalized form and (3) It behaves gracefully in many scenarios where the classical expansion converges poorly. We show that the Gaussian bias model describes the galaxy environment distribution $p(\delta | \mathrm{g})$, the scale dependent bias function $f$ and the renormalized bias function $F$ of haloes and galaxies generally equally well or significantly better than a second order expansion with the same number of parameters. We suggest that a Gaussian bias approach may enhance the range of validity of bias schemes where the canonical expansion converges poorly and further, that it may make new applications possible, since it guarantees the positivity of predicted galaxy densities., Comment: 21 pages, 12 figures, submitted to A&A

The spatial distribution of galaxies is a highly complex phenomenon currently impossible to predict deterministically. However, by using a statistical $\textit{bias}$ relation, it becomes possible to robustly model the average abundance of galaxies as a function of the underlying matter density field. Understanding the properties and parametric description of the bias relation is key to extract cosmological information from future galaxy surveys. Here, we contribute to this topic primarily in two ways: (1) We develop a new set of probabilistic estimators for bias parameters using the moments of the Lagrangian galaxy environment distribution. These estimators include spatial corrections at different orders to measure bias parameters independently of the damping scale. We report robust measurements of a variety of bias parameters for haloes, including the tidal bias and its dependence with spin at a fixed mass. (2) We propose an alternative formulation of the bias expansion in terms of "cumulant bias parameters" that describe the response of the logarithmic galaxy density to large-scale perturbations. We find that cumulant biases of haloes are consistent with zero at orders $n > 2$. This suggests that: (i) previously reported bias relations at order $n > 2$ are an artefact of the entangled basis of the canonical bias expansion; (ii) the convergence of the bias expansion may be improved by phrasing it in terms of cumulants; (iii) the bias function is very well approximated by a Gaussian -- an avenue which we explore in a companion paper., Comment: 26 pages, 16 figures, submitted to A&A

The intrinsic alignment of galaxies is an important ingredient for modelling weak-lensing measurements, and a potentially valuable cosmological and astrophysical signal. In this paper, we present HYMALAIA: a new model to predict the intrinsic alignments of biased tracers. HYMALAIA is based on a perturbative expansion of the statistics of the Lagrangian shapes of objects, which is then advected to Eulerian space using the fully non-linear displacement field obtained from $N$-body simulations. We demonstrate that HYMALAIA is capable of consistently describing monopole and quadrupole of halo shape-shape and matter-shape correlators, and that, without increasing the number of free parameters, it does so more accurately than other perturbatively inspired models such as the non-linear alignment (NLA) model and the tidal-alignment-tidal-torquing (TATT) model., Comment: 17 pages, 9 figures. Accepted version published in MNRAS

We present an emulator that accurately predicts the power spectrum of galaxies in redshift space as a function of cosmological parameters. Our emulator is based on a 2nd-order Lagrangian bias expansion that is displaced to Eulerian space using cosmological $N$-body simulations. Redshift space distortions are then imprinted using the non-linear velocity field of simulated particles and haloes. We build the emulator using a forward neural network trained with the simulations of the BACCO project, which covers an 8-dimensional parameter space including massive neutrinos and dynamical dark energy. We show that our emulator provides unbiased cosmological constraints from the monopole, quadrupole, and hexadecapole of a mock galaxy catalogue that mimics the BOSS-CMASS sample down to nonlinear scales ($k\sim0.6$[$h/$Mpc]$^{3}$). This work opens up the possibility of robustly extracting cosmological information from small scales using observations of the large-scale structure of the Universe., Comment: 16 pages, 9 figures

Cosmological $N$-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires correspondingly lower statistical uncertainties in simulations, usually achieved by increasing simulation sizes at the expense of computational power. It was recently proposed to reduce simulation variance without incurring additional computational costs by adopting fixed-amplitude initial conditions. This method has been demonstrated not to introduce bias in various statistics, including the two-point statistics of galaxy samples typically used for extracting cosmological parameters from galaxy redshift survey data, but requires us to revisit current methods for estimating covariance matrices of clustering statistics for simulations. In this work, we find that it is not trivial to construct covariance matrices analytically for fixed-amplitude simulations, but we demonstrate that EZmock (Effective Zel'dovich approximation mock catalogue), the most efficient method for constructing mock catalogues with accurate two- and three-point statistics, provides reasonable covariance matrix estimates for such simulations. We further examine how the variance suppression obtained by amplitude-fixing depends on three-point clustering, small-scale clustering, and galaxy bias, and propose intuitive explanations for the effects we observe based on the EZmock bias model., Comment: 9 pages, 7 figures; in v2 we incorporate minor modifications from peer review and copyediting

We study the relations among the parameters of the hybrid Lagrangian bias expansion model, fitting biased auto and cross power spectra up to $k_{\rm max} = 0.7 \, h \, \mathrm{Mpc}^{-1}$. We consider $\sim 8000$ halo and galaxy samples, with different halo masses, redshifts, galaxy number densities, and varying the parameters of the galaxy formation model. Galaxy samples are obtained through state-of-the-art extended subhalo abundance matching techniques and include both stellar-mass and star-formation-rate selected galaxies. All of these synthetic galaxies samples are publicly available at https://bacco.dipc.org/galpk.html. We find that the hybrid Lagrangian bias model provides accurate fits to all of our halo and galaxy samples. The coevolution relations between galaxy bias parameters, although roughly compatible with those obtained for haloes, show systematic shifts and larger scatter. We explore possible sources of this difference in terms of dependence on halo occupation and assembly bias of each sample. The bias parameter relations displayed in this work can be used as a prior for future Bayesian analyses employing the hybrid Lagrangian bias expansion model., Comment: 14 pages, 12 figures, galaxy power spectra available at https://bacco.dipc.org/galpk.html

Improving the theoretical description of galaxy clustering on small scales is an important challenge in cosmology, as it can considerably increase the scientific return of forthcoming galaxy surveys -- e.g. tightening the bounds on neutrino masses and deviations from general relativity. In this paper, we propose and test a new model for the clustering of galaxies that is able to accurately describe redshift-space distortions even down to small scales. This model corresponds to a second-order perturbative Lagrangian bias expansion which is advected to Eulerian space employing a displacement field extracted from $N$-body simulations. Eulerian coordinates are then transformed into redshift space by directly employing simulated velocity fields augmented with nuisance parameters capturing various possible satellite fractions and intra-halo small-scale velocities. We quantify the accuracy of our approach against samples of physically-motivated mock galaxies selected according to either Stellar Mass (SM) or Star Formation Rate (SFR) at multiple abundances and at $z=0$ and $1$. We find our model describes the monopole, quadrupole, and hexadecapole of the galaxy-power spectra down to scales of $k\approx 0.6 [h/$Mpc] within the accuracy of our simulations. This approach could pave the way to significantly increase the amount of cosmological information to be extracted from future galaxy surveys., Comment: 15 pages, 8 figures

We present an emulator for the two-point clustering of biased tracers in real space. We construct this emulator using neural networks calibrated with more than $400$ cosmological models in a 8-dimensional cosmological parameter space that includes massive neutrinos an dynamical dark energy. The properties of biased tracers are described via a Lagrangian perturbative bias expansion which is advected to Eulerian space using the displacement field of numerical simulations. The cosmology-dependence is captured thanks to a cosmology-rescaling algorithm. We show that our emulator is capable of describing the power spectrum of galaxy formation simulations for a sample mimicking that of a typical Emission-Line survey at $z \sim 1$ with an accuracy of $1-2\%$ up to nonlinear scales $k \sim 0.7 h \mathrm{Mpc}^{-1}$., Comment: 14 pages, 8 figures

We present a neural-network emulator for baryonic effects in the non-linear matter power spectrum. We calibrate this emulator using more than 50,000 measurements in a 15-dimensional parameters space, varying cosmology and baryonic physics. Baryonic physics is described through a baryonification algorithm, that has been shown to accurately capture the relevant effects on the power spectrum and bispectrum in state-of-the-art hydrodynamical simulations. Cosmological parameters are sampled using a cosmology-rescaling approach including massive neutrinos and dynamical dark energy. The specific quantity we emulate is the ratio between matter power spectrum with baryons and gravity-only, and we estimate the overall precision of the emulator to be 1-2%, at all scales 0.01 < k < 5 h/Mpc, and redshifts 0 < z < 1.5. We also obtain an accuracy of 1-2%, when testing the emulator against a collection of 74 different cosmological hydrodynamical simulations and their respective gravity-only counterparts. We show also that only one baryonic parameter, namely Mc, which set the gas fraction retained per halo mass, is enough to have accurate and realistic predictions of the baryonic feedback at a given epoch. Our emulator will become publicly available in http://www.dipc.org/bacco., Comment: 13 pages, 11 figures. Comments are welcome

This work investigates the connection between the cosmic web and the halo distribution through the gravitational potential at the field level. We combine three fields of research, cosmic web classification, perturbation theory expansions of the halo bias, and halo (galaxy) mock catalogue making methods. In particular, we use the invariants of the tidal field and the velocity shear tensor as generating functions to reproduce the halo number counts of a reference catalogue from full gravity calculations, populating the dark matter field on a mesh well into the non-linear regime ($3\,h^{-1}\,{\rm Mpc}$ scales). Our results show an unprecedented agreement with the reference power spectrum within 1% up to $k=0.72\,h\,{\rm Mpc}^{-1}$. By analysing the three-point statistics on large scales (configurations of up to $k=0.2\,h\,{\rm Mpc}^{-1}$), we find evidence for non-local bias at the 4.8 $\sigma$ confidence level, being compatible with the reference catalogue. In particular, we find that a detailed description of tidal anisotropic clustering on large scales is crucial to achieve this accuracy at the field level. These findings can be particularly important for the analysis of the next generation of galaxy surveys in mock galaxy production., Comment: 19 pages, 10 figures and 2 tables, accepted for publication at MNRAS

We present the BACCO project, a simulation framework specially designed to provide highly-accurate predictions for the distribution of mass, galaxies, and gas as a function of cosmological parameters. In this paper, we describe our main suite of simulations (L $\sim2$ Gpc and $4320^3$ particles) and present various validation tests. Using a cosmology-rescaling technique, we predict the nonlinear mass power spectrum over the redshift range $0

The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard Bayesian algorithms for cosmological inferences, such as MCMC, might become inadequate. Here, we propose a new approach to parameter estimation based on an iterative Gaussian emulation of the target likelihood function. This requires a minimal number of likelihood evaluations and naturally accommodates for stochasticity in theoretical models. We apply the algorithm to estimate 9 parameters from the monopole and quadrupole of a mock power spectrum in redshift space. We obtain accurate posterior distribution functions with approximately 100 times fewer likelihood evaluations than an affine invariant MCMC, roughly independently from the dimensionality of the problem. We anticipate that our parameter estimation algorithm will accelerate the adoption of more accurate theoretical models in data analysis, enabling more comprehensive exploitation of cosmological observables., Comment: 12 pages, 5 figures

We present and test a framework that models the three-dimensional distribution of mass in the Universe as a function of cosmological and astrophysical parameters. Our approach combines two different techniques: a rescaling algorithm that modifies the cosmology of gravity-only N-body simulations, and a baryonification algorithm which mimics the effects of astrophysical processes induced by baryons, such as star formation and AGN feedback. We show how this approach can accurately reproduce the effects of baryons on the matter power spectrum of various state-of-the-art hydro-dynamical simulations (EAGLE, Illustris, Illustris-TNG, Horizon-AGN, and OWLS,Cosmo-OWLS and BAHAMAS), to percent level from very large down to small, highly nonlinear scales, k= 5 h/Mpc, and from z=0 up to z=2. We highlight that, thanks to the heavy optimisation of the algorithms, we can obtain these predictions for arbitrary baryonic models and cosmology (including massive neutrinos and dynamical dark energy models) with an almost negligible CPU cost. Therefore, this approach is efficient enough for cosmological data analyses. With these tools in hand we explore the degeneracies between cosmological and astrophysical parameters in the nonlinear mass power spectrum. Our findings suggest that after marginalising over baryonic physics, cosmological constraints inferred from weak gravitational lensing should be moderately degraded., Comment: 20 pages, 15 figures. Submitted to MNRAS

In this paper we demonstrate that the information encoded in \emph{one} single (sufficiently large) $N$-body simulation can be used to reproduce arbitrary numbers of halo catalogues, using approximated realisations of dark matter density fields with different initial conditions. To this end we use as a reference one realisation (from an ensemble of $300$) of the Minerva $N$-body simulations and the recently published Bias Assignment Method to extract the local and non-local bias linking the halo to the dark matter distribution. We use an approximate (and fast) gravity solver to generate $300$ dark matter density fields from the down-sampled initial conditions of the reference simulation and sample each of these fields using the halo-bias and a kernel, both calibrated from the arbitrarily chosen realisation of the reference simulation. We show that the power spectrum, its variance and the three-point statistics are reproduced within $\sim 2\%$ (up to $k\sim1.0\,h\,{\rm Mpc}^{-1}$), $\sim 5-10\%$ and $\sim 10\%$, respectively. Using a model for the real space power spectrum (with three free bias parameters), we show that the covariance matrices obtained from our procedure lead to parameter uncertainties that are compatible within $\sim 10\%$ with respect to those derived from the reference covariance matrix, and motivate approaches that can help to reduce these differences to $\sim 1\%$. Our method has the potential to learn from one simulation with moderate volumes and high-mass resolution and extrapolate the information of the bias and the kernel to larger volumes, making it ideal for the construction of mock catalogues for present and forthcoming observational campaigns such as Euclid or DESI., Comment: Accepted for publication at MNRAS

Providing accurate predictions for the spatial distribution of matter and luminous tracers in the presence of massive neutrinos is an important task, given the imminent arrival of highly accurate large-scale structure observations. In this work, we address this challenge by extending cosmology-rescaling algorithms to massive neutrino cosmologies. In this way, a $\Lambda$CDM simulation can be modified to provide nonlinear structure formation predictions in the presence a hot component of arbitrary mass, and, if desired, to include non-gravitational modifications to the clustering of matter on large scales. We test the accuracy of the method by comparing its predictions to a suite of simulations carried out explicitly including a neutrino component in its evolution equations. We find that, for neutrino masses in the range $M_\nu \in [0.06, 0.3] ~ \mathrm{eV}$ the matter power spectrum is recovered to better than $1\%$ on all scales $k<2~h~\mathrm{Mpc}^{-1}$. Similarly, the halo mass function is predicted at a few percent level over the range $M_{\rm halo} \in [10^{12}, 10^{15}] ~ h^{-1} ~ \mathrm{M}_{\odot}$, and so do also the multipoles of the galaxy 2-point correlation function in redshift space over $r \in [0.1, 200] ~ h^{-1} ~ \mathrm{Mpc}$. We provide parametric forms for the necessary transformations, as a function of $\Omega_{\rm m}$ and $\Omega_{\nu}$ for various target redshifts., Comment: 15 pages, 11 figures

We present the UNIT $N$-body cosmological simulations project, designed to provide precise predictions for nonlinear statistics of the galaxy distribution. We focus on characterizing statistics relevant to emission line and luminous red galaxies in the current and upcoming generation of galaxy surveys. We use a suite of precise particle mesh simulations (FastPM) as well as with full $N$-body calculations with a mass resolution of $\sim 1.2\times10^9\,h^{-1}$M$_{\odot}$ to investigate the recently suggested technique of Angulo & Pontzen 2016 to suppress the variance of cosmological simulations We study redshift space distortions, cosmic voids, higher order statistics from $z=2$ down to $z=0$. We find that both two- and three-point statistics are unbiased. Over the scales of interest for baryon acoustic oscillations and redshift-space distortions, we find that the variance is greatly reduced in the two-point statistics and in the cross correlation between halos and cosmic voids, but is not reduced significantly for the three-point statistics. We demonstrate that the accuracy of the two-point correlation function for a galaxy survey with effective volume of 20 ($h^{-1}$Gpc)$^3$ is improved by about a factor of 40, indicating that two pairs of simulations with a volume of 1 ($h^{-1}$Gpc)$^3$ lead to the equivalent variance of $\sim$150 such simulations. The $N$-body simulations presented here thus provide an effective survey volume of about seven times the effective survey volume of DESI or Euclid. The data from this project, including dark matter fields, halo catalogues, and their clustering statistics, are publicly available at http://www.unitsims.org., Comment: 12 pages, 9 figures. This version matches the one accepted by MNRAS. The data from this project are publicly available at: http://www.unitsims.org

We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogs to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of three-hundred realisations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and nonlinear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10% of the errors estimated from N-body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to two-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N-body simulation, and therefore to the bispectrum variance, by comparing with a larger set of several thousands realisations performed with one approximate method., Comment: Additional results with respect to v1, new section and new figures added. 25 pages, 1 table 18 figures

We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constrains related to growth rate of structure, Alcock-Paczynski distortions and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE-COLA, Pinocchio and PeakPatch), methods that rely on halo assignment schemes onto dark-matter overdensities calibrated with a target N-body run (Halogen, Patchy) and two standard assumptions about the full density PDF (Gaussian and Lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5\%$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10\%$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10\%$ of those from the N-body based covariance., Comment: 20 pages, 16 figures, replaced to match accepted MNRAS version. Results on parameter errors changed

This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic two-point correlation function measurements. Our comparison includes seven approximate methods, which can be divided into three categories: predictive methods that follow the evolution of the linear density field deterministically (ICE-COLA, Peak Patch, and Pinocchio), methods that require a calibration with N-body simulations (Patchy and Halogen), and simpler recipes based on assumptions regarding the shape of the probability distribution function (PDF) of density fluctuations (log-normal and Gaussian density fields). We analyse the impact of using covariance estimates obtained from these approximate methods on cosmological analyses of galaxy clustering measurements, using as a reference the covariances inferred from a set of full N-body simulations. We find that all approximate methods can accurately recover the mean parameter values inferred using the N-body covariances. The obtained parameter uncertainties typically agree with the corresponding N-body results within 5% for our lower mass threshold, and 10% for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20% depending on whether the halo samples used to define the covariance matrices are defined by matching the mass, number density, or clustering amplitude of the parent N-body samples. The results of our configuration-space analysis indicate that most approximate methods provide similar results, with no single method clearly outperforming the others., Comment: 23 pages, 11 figures. Replaced to match accepted MNRAS version. Included Kullback-Leibler divergence

We develop a methodology to optimise the measurement of Baryon Acoustic Oscillation (BAO) from a given galaxy sample. In our previous work, we demonstrated that one can measure BAO from tracers in under-dense regions (voids). In this study, we combine the over-dense and under-dense tracers (galaxies & voids) to obtain better constraints on the BAO scale. To this end, we modify the de-wiggled BAO model with an additional parameter to describe both the BAO peak and the underlying exclusion pattern of void 2PCFs. We show that after applying BAO reconstruction to galaxies, the BAO peak scale of both galaxies and voids are unbiased using the modified model. Furthermore, we use a new 2PCF estimator for a multi-tracer analysis with galaxies and voids. In simulations, the joint sample improves by about 10% the constraint for the post-reconstruction BAO peak position compared to the result from galaxies alone, which is equivalent to an enlargement of the survey volume by 20%. Applying this method to the BOSS DR12 data, we have an 18% improvement for the low-z sample (0.2

We perform a tomographic analysis of structure growth and expansion rate from the anisotropic galaxy clustering of the combined sample of Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, which covers the redshift range of $0.2

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since July 2014. This paper describes the second data release from this phase, and the fourteenth from SDSS overall (making this, Data Release Fourteen or DR14). This release makes public data taken by SDSS-IV in its first two years of operation (July 2014-2016). Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS); the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data driven machine learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS website (www.sdss.org) has been updated for this release, and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020, and will be followed by SDSS-V., Comment: SDSS-IV collaboration alphabetical author data release paper. DR14 happened on 31st July 2017. 19 pages, 5 figures. Accepted by ApJS on 28th Nov 2017 (this is the "post-print" and "post-proofs" version; minor corrections only from v1, and most of errors found in proofs corrected)

We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147,000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts $0.8 < z < 2.2$ and measure their spherically-averaged clustering in both configuration and Fourier space. Our observational dataset and the 1400 simulated realizations of the dataset allow us to detect a preference for BAO that is greater than 2.8$\sigma$. We determine the spherically averaged BAO distance to $z = 1.52$ to 3.8 per cent precision: $D_V(z=1.52)=3843\pm147 \left(r_{\rm d}/r_{\rm d, fid}\right)\ $Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flat $\Lambda$CDM best-fit cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find $\Omega_{\Lambda} > 0$ at 6.6$\sigma$ significance when testing a $\Lambda$CDM model with free curvature., Comment: Accepted by MNRAS; BAO distance likelihood available in source files 'QSOv1.9fEZmock_BAOchi2.dat'; full set of data to be public eventually from SDSS website

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., Comment: Published in Astronomical Journal

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) began observations in July 2014. It pursues three core programs: APOGEE-2, MaNGA, and eBOSS. In addition, eBOSS contains two major subprograms: TDSS and SPIDERS. This paper describes the first data release from SDSS-IV, Data Release 13 (DR13), which contains new data, reanalysis of existing data sets and, like all SDSS data releases, is inclusive of previously released data. DR13 makes publicly available 1390 spatially resolved integral field unit observations of nearby galaxies from MaNGA, the first data released from this survey. It includes new observations from eBOSS, completing SEQUELS. In addition to targeting galaxies and quasars, SEQUELS also targeted variability-selected objects from TDSS and X-ray selected objects from SPIDERS. DR13 includes new reductions of the SDSS-III BOSS data, improving the spectrophotometric calibration and redshift classification. DR13 releases new reductions of the APOGEE-1 data from SDSS-III, with abundances of elements not previously included and improved stellar parameters for dwarf stars and cooler stars. For the SDSS imaging data, DR13 provides new, more robust and precise photometric calibrations. Several value-added catalogs are being released in tandem with DR13, in particular target catalogs relevant for eBOSS, TDSS, and SPIDERS, and an updated red-clump catalog for APOGEE. This paper describes the location and format of the data now publicly available, as well as providing references to the important technical papers that describe the targeting, observing, and data reduction. The SDSS website, http://www.sdss.org, provides links to the data, tutorials and examples of data access, and extensive documentation of the reduction and analysis procedures. DR13 is the first of a scheduled set that will contain new data and analyses from the planned ~6-year operations of SDSS-IV., Comment: Full information on DR13 available at http://www.sdss.org. Comments welcome to spokesperson@sdss.org. To be published in ApJS

We develop a new methodology called double-probe analysis with the aim of minimizing informative priors in the estimation of cosmological parameters. We extract the dark-energy-model-independent cosmological constraints from the joint data sets of Baryon Oscillation Spectroscopic Survey (BOSS) galaxy sample and Planck cosmic microwave background (CMB) measurement. We measure the mean values and covariance matrix of $\{R$, $l_a$, $\Omega_b h^2$, $n_s$, $log(A_s)$, $\Omega_k$, $H(z)$, $D_A(z)$, $f(z)\sigma_8(z)\}$, which give an efficient summary of Planck data and 2-point statistics from BOSS galaxy sample, where $R=\sqrt{\Omega_m H_0^2}\,r(z_*)$, and $l_a=\pi r(z_*)/r_s(z_*)$, $z_*$ is the redshift at the last scattering surface, and $r(z_*)$ and $r_s(z_*)$ denote our comoving distance to $z_*$ and sound horizon at $z_*$ respectively. The advantage of this method is that we do not need to put informative priors on the cosmological parameters that galaxy clustering is not able to constrain well, i.e. $\Omega_b h^2$ and $n_s$. Using our double-probe results, we obtain $\Omega_m=0.304\pm0.009$, $H_0=68.2\pm0.7$, and $\sigma_8=0.806\pm0.014$ assuming $\Lambda$CDM; and $\Omega_k=0.002\pm0.003$ and $w=-1.00\pm0.07$ assuming o$w$CDM. The results show no tension with the flat $\Lambda$CDM cosmological paradigm. By comparing with the full-likelihood analyses with fixed dark energy models, we demonstrate that the double-probe method provides robust cosmological parameter constraints which can be conveniently used to study dark energy models. We extend our study to measure the sum of neutrino mass and obtain $\Sigma m_\nu<0.10/0.22$ (68\%/95\%) assuming $\Lambda$CDM and $\Sigma m_\nu<0.26/0.52$ (68\%/95\%) assuming $w$CDM. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS., Comment: 19 pages, 17 figures

We present cosmological results from the final galaxy clustering data set of the Baryon Oscillation Spectroscopic Survey, part of the Sloan Digital Sky Survey III. Our combined galaxy sample comprises 1.2 million massive galaxies over an effective area of 9329 deg^2 and volume of 18.7 Gpc^3, divided into three partially overlapping redshift slices centred at effective redshifts 0.38, 0.51, and 0.61. We measure the angular diameter distance DM and Hubble parameter H from the baryon acoustic oscillation (BAO) method after applying reconstruction to reduce non-linear effects on the BAO feature. Using the anisotropic clustering of the pre-reconstruction density field, we measure the product DM*H from the Alcock-Paczynski (AP) effect and the growth of structure, quantified by f{\sigma}8(z), from redshift-space distortions (RSD). We combine measurements presented in seven companion papers into a set of consensus values and likelihoods, obtaining constraints that are tighter and more robust than those from any one method. Combined with Planck 2015 cosmic microwave background measurements, our distance scale measurements simultaneously imply curvature {\Omega}_K =0.0003+/-0.0026 and a dark energy equation of state parameter w = -1.01+/-0.06, in strong affirmation of the spatially flat cold dark matter model with a cosmological constant ({\Lambda}CDM). Our RSD measurements of f{\sigma}_8, at 6 per cent precision, are similarly consistent with this model. When combined with supernova Ia data, we find H0 = 67.3+/-1.0 km/s/Mpc even for our most general dark energy model, in tension with some direct measurements. Adding extra relativistic species as a degree of freedom loosens the constraint only slightly, to H0 = 67.8+/-1.2 km/s/Mpc. Assuming flat {\Lambda}CDM we find {\Omega}_m = 0.310+/-0.005 and H0 = 67.6+/-0.5 km/s/Mpc, and we find a 95% upper limit of 0.16 eV/c^2 on the neutrino mass sum., Comment: 38 pages, 20 figures, 12 tables. Submitted to MNRAS. Clustering data and likelihoods are made available at https://sdss3.org/science/boss_publications.php

We present baryon acoustic oscillation (BAO) scale measurements determined from the clustering of 1.2 million massive galaxies with redshifts 0.2 < z < 0.75 distributed over 9300 square degrees, as quantified by their redshift-space correlation function. In order to facilitate these measurements, we define, describe, and motivate the selection function for galaxies in the final data release (DR12) of the SDSS III Baryon Oscillation Spectroscopic Survey (BOSS). This includes the observational footprint, masks for image quality and Galactic extinction, and weights to account for density relationships intrinsic to the imaging and spectroscopic portions of the survey. We simulate the observed systematic trends in mock galaxy samples and demonstrate that they impart no bias on baryon acoustic oscillation (BAO) scale measurements and have a minor impact on the recovered statistical uncertainty. We measure transverse and radial BAO distance measurements in 0.2 < z < 0.5, 0.5 < z < 0.75, and (overlapping) 0.4 < z < 0.6 redshift bins. In each redshift bin, we obtain a precision that is 2.7 per cent or better on the radial distance and 1.6 per cent or better on the transverse distance. The combination of the redshift bins represents 1.8 per cent precision on the radial distance and 1.1 per cent precision on the transverse distance. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. (2016) to produce the final cosmological constraints from BOSS., Comment: Matches version accepted by MNRAS

We analyse the broad-range shape of the monopole and quadrupole correlation functions of the BOSS Data Release 12 (DR12) CMASS and LOWZ galaxy sample to obtain constraints on the Hubble expansion rate $H(z)$, the angular-diameter distance $D_A(z)$, the normalised growth rate $f(z)\sigma_8(z)$, and the physical matter density $\Omega_mh^2$. We adopt wide and flat priors on all model parameters in order to ensure the results are those of a `single-probe' galaxy clustering analysis. We also marginalise over three nuisance terms that account for potential observational systematics affecting the measured monopole. However, such Monte Carlo Markov Chain analysis is computationally expensive for advanced theoretical models, thus we develop a new methodology to speed up our analysis. We obtain $\{D_A(z)r_{s,fid}/r_s$Mpc, $H(z)r_s/r_{s,fid}$kms$^{-1}$Mpc$^{-1}$, $f(z)\sigma_8(z)$, $\Omega_m h^2\}$ = $\{956\pm28$ , $75.0\pm4.0$ , $0.397 \pm 0.073$, $0.143\pm0.017\}$ at $z=0.32$ and $\{1421\pm23$, $96.7\pm2.7$ , $0.497 \pm 0.058$, $0.137\pm0.015\}$ at $z=0.59$ where $r_s$ is the comoving sound horizon at the drag epoch and $r_{s,fid}=147.66$Mpc for the fiducial cosmology in this study. In addition, we divide the galaxy sample into four redshift bins to increase the sensitivity of redshift evolution. However, we do not find improvements in terms of constraining dark energy model parameters. Combining our measurements with Planck data, we obtain $\Omega_m=0.306\pm0.009$, $H_0=67.9\pm0.7$kms$^{-1}$Mpc$^{-1}$, and $\sigma_8=0.815\pm0.009$ assuming $\Lambda$CDM; $\Omega_k=0.000\pm0.003$ assuming oCDM; $w=-1.01\pm0.06$ assuming $w$CDM; and $w_0=-0.95\pm0.22$ and $w_a=-0.22\pm0.63$ assuming $w_0w_a$CDM. Our results show no tension with the flat $\Lambda$CDM cosmological paradigm. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS., Comment: 22 pages, 11 figures

The existence of a cosmic neutrino background can be probed indirectly by CMB experiments, not only by measuring the background density of radiation in the universe, but also by searching for the typical signatures of the fluctuations of free-streaming species in the temperature and polarisation power spectrum. Previous studies have already proposed a rather generic parametrisation of these fluctuations, that could help to discriminate between the signature of ordinary free-streaming neutrinos, or of more exotic dark radiation models. Current data are compatible with standard values of these parameters, which seems to bring further evidence for the existence of a cosmic neutrino background. In this work, we investigate the robustness of this conclusion under various assumptions. We generalise the definition of an effective sound speed and viscosity speed to the case of massive neutrinos or other dark radiation components experiencing a non-relativistic transition. We show that current bounds on these effective parameters do not vary significantly when considering an arbitrary value of the particle mass, or extended cosmological models with a free effective neutrino number, dynamical dark energy or a running of the primordial spectrum tilt. We conclude that it is possible to make a robust statement about the detection of the cosmic neutrino background by CMB experiments., Comment: version accepted for publication in JCAP. 19 pages, 7 figures, 3 tables. Minor changes. References added

We derive constraints on cosmological parameters and tests of dark energy models from the combination of baryon acoustic oscillation (BAO) measurements with cosmic microwave background (CMB) and Type Ia supernova (SN) data. We take advantage of high-precision BAO measurements from galaxy clustering and the Ly-alpha forest (LyaF) in the BOSS survey of SDSS-III. BAO data alone yield a high confidence detection of dark energy, and in combination with the CMB angular acoustic scale they further imply a nearly flat universe. Combining BAO and SN data into an "inverse distance ladder" yields a 1.7% measurement of $H_0=67.3 \pm1.1$ km/s/Mpc. This measurement assumes standard pre-recombination physics but is insensitive to assumptions about dark energy or space curvature, so agreement with CMB-based estimates that assume a flat LCDM cosmology is an important corroboration of this minimal cosmological model. For open LCDM, our BAO+SN+CMB combination yields $\Omega_m=0.301 \pm 0.008$ and curvature $\Omega_k=-0.003 \pm 0.003$. When we allow more general forms of evolving dark energy, the BAO+SN+CMB parameter constraints remain consistent with flat LCDM. While the overall $\chi^2$ of model fits is satisfactory, the LyaF BAO measurements are in moderate (2-2.5 sigma) tension with model predictions. Models with early dark energy that tracks the dominant energy component at high redshifts remain consistent with our constraints. Expansion history alone yields an upper limit of 0.56 eV on the summed mass of neutrino species, improving to 0.26 eV if we include Planck CMB lensing. Standard dark energy models constrained by our data predict a level of matter clustering that is high compared to most, but not all, observational estimates. (Abridged), Comment: 38 pages, 20 figures, BOSS collaboration paper; v2: fixed inconsistent definitions of DH, added references; v3: version accepted by PRD, corrected error resulting in significantly weaker constraints on decaying dark matter model

With the largest spectroscopic galaxy survey volume drawn from the SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS), we can extract cosmological constraints from the measurements of redshift and geometric distortions at quasi-linear scales (e.g. above 50 $h^{-1}$Mpc). We analyze the broad-range shape of the monopole and quadrupole correlation functions of the BOSS Data Release 12 (DR12) CMASS galaxy sample, at the effective redshift $z=0.59$, to obtain constraints on the Hubble expansion rate $H(z)$, the angular-diameter distance $D_A(z)$, the normalized growth rate $f(z)\sigma_8(z)$, and the physical matter density $\Omega_mh^2$. We obtain robust measurements by including a polynomial as the model for the systematic errors, and find it works very well against the systematic effects, e.g., ones induced by stars and seeing. We provide accurate measurements $\{D_A(0.59)r_{s,fid}/r_s$ $\rm Mpc$, $H(0.59)r_s/r_{s,fid}$ $km s^{-1} Mpc^{-1}$, $f(0.59)\sigma_8(0.59)$, $\Omega_m h^2\}$ = $\{1427\pm26$, $97.3\pm3.3$, $0.488 \pm 0.060$, $0.135\pm0.016\}$, where $r_s$ is the comoving sound horizon at the drag epoch and $r_{s,fid}=147.66$ Mpc is the sound scale of the fiducial cosmology used in this study. The parameters which are not well constrained by our galaxy clustering analysis are marginalized over with wide flat priors. Since no priors from other data sets, e.g., cosmic microwave background (CMB), are adopted and no dark energy models are assumed, our results from BOSS CMASS galaxy clustering alone may be combined with other data sets, i.e., CMB, SNe, lensing or other galaxy clustering data to constrain the parameters of a given cosmological model. The uncertainty on the dark energy equation of state parameter, $w$, from CMB+CMASS is about 8 per cent. The uncertainty on the curvature fraction, $\Omega_k$, is 0.3 per cent. We do not find deviation from flat $\Lambda$CDM., Comment: 15 pages, 11 figures. The latest version matches and the accepted version by MNRAS. A bug in the first version has been identified and fixed in the new version. We have redone the analysis with newest data (BOSS DR12)