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Francisco Prada

Publications and source records attributed to Francisco Prada.

At least 181 records · Page 10Linked to original sources

Gravitational perturbations of the Higgs field

We study the possible effects of classical gravitational backgrounds on the Higgs field through the modifications induced in the one-loop effective potential and the vacuum expectation value of the energy-momentum tensor. We concentrate our study on the Higgs self-interaction contribution in a perturbed FRW metric. For weak and slowly varying gravitational fields, a complete set of mode solutions for the Klein-Gordon equation is obtained to leading order in the adiabatic approximation. Dimensional regularization has been used in the integral evaluation and a detailed study of the integration of nonrational functions in this formalism has been presented. As expected, the regularized effective potential contains the same divergences as in flat spacetime, which can be renormalized without the need of additional counterterms. We find that, in contrast with other regularization methods, even though metric perturbations affect the mode solutions, they do not contribute to the leading adiabatic order of the potential. We also obtain explicit expressions of the complete energy-momentum tensor for general nonminimal coupling in terms of the perturbed modes. The corresponding leading adiabatic contributions are also obtained.

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Clustering of quasars in the First Year of the SDSS-IV eBOSS survey: Interpretation and halo occupation distribution

In current and future surveys, quasars play a key role. The new data will extend our knowledge of the Universe as it will be used to better constrain the cosmological model at redshift $z>1$ via baryon acoustic oscillation and redshift space distortion measurements. Here, we present the first clustering study of quasars observed by the extended Baryon Oscillation Spectroscopic Survey. We measure the clustering of $\sim 70,000$ quasars located in the redshift range $0.9<z<2.2$ that cover 1,168 deg$^2$. We model the clustering and produce high-fidelity quasar mock catalogues based on the BigMultiDark Planck simulation. Thus, we use a modified (Sub)Halo Abundance Matching model to account for the specificities of the halo population hosting quasars. We find that quasars are hosted by halos with masses $\sim10^{12.7}M_\odot$ and their bias evolves from 1.54 ($z=1.06$) to 3.15 ($z=1.98$). Using the current eBOSS data, we cannot distinguish between models with different fractions of satellites. The high-fidelity mock light-cones, including properties of halos hosting quasars, are made publicly available.

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Characterization of subhalo structural properties and implications for dark matter annihilation signals

A prediction of the standard LCDM cosmology is that dark matter (DM) halos are teeming with numerous self-bound substructure, or subhalos. The precise properties of these subhalos represent important probes of the underlying cosmological model. We use data from Via Lactea II and ELVIS N-body simulations to learn about the structure of subhalos with masses 1e6 - 1e11 Msun/h. Thanks to a superb subhalo statistics, we study subhalo properties as a function of distance to host halo center and subhalo mass, and provide a set of fits that accurately describe the subhalo structure. We also investigate the role of subhalos on the search for DM annihilation. Previous work has shown that subhalos are expected to boost the DM signal of their host halos significantly. Yet, these works traditionally assumed that subhalos exhibit similar structural properties than those of field halos, while it is known that subhalos are more concentrated. Building upon our N-body data analysis, we refine the substructure boost model of Sanchez-Conde & Prada (2014), and find boosts that are a factor 2-3 higher. We further refine the model to include unavoidable tidal stripping effects on the subhalo population. For field halos, this introduces a moderate 20-30% suppression. Yet, for subhalos like those hosting dwarf galaxy satellites, tidal stripping plays a critical role, the boost being at the level of a few tens of percent at most. We provide a parametrization of the boost for field halos that can be safely applied over a wide halo mass range.

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Dark matter statistics for large galaxy catalogs: power spectra and covariance matrices

Upcoming and existing large-scale surveys of galaxies require accurate theoretical predictions of the dark matter clustering statistics for thousands of mock galaxy catalogs. We demonstrate that this goal can be achieve with our new Parallel Particle-Mesh (PM) Nbody code (PPM-GLAM) at a very low computational cost. We run about 15,000 simulations with ~2 billion particles that provide ~1% accuracy of the dark matter power spectra P(k) for wave-numbers up to k~ 1h/Mpc. Using this large data-set we study the power spectrum covariance matrix, the stepping stone for producing mock catalogs. In contrast to many previous analytical and numerical results, we find that the covariance matrix normalised to the power spectrum C(k,k')/P(k)P(k') has a complex structure of non-diagonal components. It has an upturn at small k, followed by a minimum at k=0.1-0.2h/Mpc. It also has a maximum at k=0.5-0.6h/Mpc. The normalised covariance matrix strongly evolves with redshift: C(k,k')~delta(t)^alpha P(k)P(k'), where delta is the linear growth factor and alpha ~ 1-1.25, which indicates that the covariance matrix depends on cosmological parameters. We also show that waves longer than 1Gpc have very little impact on the power spectrum and covariance matrix. This significantly reduces the computational costs and complexity of theoretical predictions: relatively small volume ~ (1Gpc)^3 simulations capture the necessary properties of dark matter clustering statistics. All the power spectra obtained from many thousands of our simulations are publicly available.

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The Clustering of Galaxies in the Completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmic Flows and Cosmic Web from Luminous Red Galaxies

We present a Bayesian phase-space reconstruction of the cosmic large-scale matter density and velocity fields from the SDSS-III Baryon Oscillations Spectroscopic Survey Data Release 12 (BOSS DR12) CMASS galaxy clustering catalogue. We rely on a given $Λ$CDM cosmology, a mesh resolution in the range of 6-10 $h^{-1}$ Mpc, and a lognormal-Poisson model with a redshift dependent nonlinear bias. The bias parameters are derived from the data and a general renormalised perturbation theory approach. We use combined Gibbs and Hamiltonian sampling, implemented in the \textsc{argo} code, to iteratively reconstruct the dark matter density field and the coherent peculiar velocities of individual galaxies, correcting hereby for coherent redshift space distortions (RSD). Our tests relying on accurate $N$-body based mock galaxy catalogues, show unbiased real space power spectra of the nonlinear density field up to $k\sim0.2\, h$ Mpc$^{-1}$, and vanishing quadrupoles down to $r\sim20\,h^{-1}$ Mpc. We also demonstrate that the nonlinear cosmic web can be obtained from the tidal field tensor based on the Gaussian component of the reconstructed density field. We find that the reconstructed velocities have a statistical correlation coefficient compared to the true velocities of each individual lightcone mock galaxy of $r\sim0.68$ including about 10% of satellite galaxies with virial motions (about $r=0.75$ without satellites). The power spectra of the velocity divergence agree well with theoretical predictions up to $k\sim0.2\,h\,{\rm Mpc}^{-1}$. This work will be especially useful to improve, e.g. BAO reconstructions, kinematic Sunyaev-Zeldovich (kSZ), integrated Sachs-Wolfe (ISW) measurements, or environmental studies.

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The angular power spectrum of the diffuse gamma-ray emission as measured by the Fermi Large Area Telescope and constraints on its Dark Matter interpretation

The isotropic gamma-ray background arises from the contribution of unresolved sources, including members of confirmed source classes and proposed gamma-ray emitters such as the radiation induced by dark matter annihilation and decay. Clues about the properties of the contributing sources are imprinted in the anisotropy characteristics of the gamma-ray background. We use 81 months of Pass 7 Reprocessed data from the Fermi Large Area Telescope to perform a measurement of the anisotropy angular power spectrum of the gamma-ray background. We analyze energies between 0.5 and 500 GeV, extending the range considered in the previous measurement based on 22 months of data. We also compute, for the first time, the cross-correlation angular power spectrum between different energy bins. We find that the derived angular spectra are compatible with being Poissonian, i.e. constant in multipole. Moreover, the energy dependence of the anisotropy suggests that the signal is due to two populations of sources, contributing, respectively, below and above 2 GeV. Finally, using data from state-of-the-art numerical simulations to model the dark matter distribution, we constrain the contribution from dark matter annihilation and decay in Galactic and extragalactic structures to the measured anisotropy. These constraints are competitive with those that can be derived from the average intensity of the isotropic gamma-ray background. Data are available at https://www-glast.stanford.edu/pub_data/552.

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The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: tomographic BAO analysis of DR12 combined sample in Fourier space

We perform a tomographic baryon acoustic oscillations (BAO) analysis using the monopole, quadrupole and hexadecapole of the redshift-space galaxy power spectrum measured from the pre-reconstructed combined galaxy sample of the completed Sloan Digital Sky Survey (SDSS-III) Baryon Oscillation Spectroscopic Survey (BOSS) Data Release (DR)12 covering the redshift range of $0.20<z<0.75$. By allowing for overlap between neighbouring redshift slices, we successfully obtained the isotropic and anisotropic BAO distance measurements within nine redshift slices to a precision of $1.5\%-3.4\%$ for $D_V/r_d$, $1.8\% -4.2\%$ for $D_A/r_d$ and $3.7\% - 7.5\%$ for $H \ r_d$, depending on effective redshifts. We provide our BAO measurement of $D_A/r_d$ and $H \ r_d$ with the full covariance matrix, which can be used for cosmological implications. Our measurements are consistent with those presented in \citet{Acacia}, in which the BAO distances are measured at three effective redshifts. We constrain dark energy parameters using our measurements, and find an improvement of the Figure-of-Merit of dark energy in general due to the temporal BAO information resolved. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.

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Higgs effective potential in a perturbed Robertson-Walker background

We calculate the one-loop effective potential of a scalar field in a Robertson-Walker background with scalar metric perturbations. A complete set of orthonormal solutions of the perturbed equations is obtained by using the adiabatic approximation for comoving observers. After analyzing the problem of renormalization in inhomogeneous backgrounds, we get the explicit contribution of metric perturbations to the effective potential. We apply these results to the Standard Model Higgs field and evaluate the effects of metric perturbations on the Higgs mass and on its vacuum expectation value. Space-time variations are found, which are proportional to the gravitational slip parameter, with a typical amplitude of the order of $Δϕ/ϕ\simeq 10^{-11}$ on cosmological scales. We also discuss possible astrophysical signatures in the Solar System and in the Milky Way that could open new possibilities to explore the symmetry breaking sector of the electroweak interactions.

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Gravitational effects on the Higgs field within the Solar System

The Higgs mechanism predicts, apart from the existence of a new scalar boson, the presence of a constant Higgs field that permeates all of space. The vacuum expectation value (VEV) of this field is affected by quantum corrections which are mainly generated by the self-interactions and couplings of the Higgs field to gauge bosons and heavy quarks. In this work we show that gravity can affect, in a non-trivial way, these quantum corrections through the finite parts of the one-loop contributions to the effective potential. In particular, we consider the corrections generated by the Standard Model Higgs self-interactions in slowly-varying weak gravitational backgrounds. The obtained results amount to the existence of non-negligible inhomogeneities in the Higgs VEV. Such inhomogeneities translate into spatial variations of the particle masses, and in particular of the proton-to-electron mass ratio. We find that these Higgs perturbations in our Solar System are controlled by the Eddington parameter, and are absent in pure General Relativity. Yet, they may be present in modified gravity theories. This predicted effect may be constrained by atomic clocks or high-resolution spectroscopic measurements, which could allow to improve current limits on modifications of Einstein's gravity.

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The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Cosmological implications of the Fourier space wedges of the final sample

We extract cosmological information from the anisotropic power spectrum measurements from the recently completed Baryon Oscillation Spectroscopic Survey (BOSS), extending the concept of clustering wedges to Fourier space. Making use of new FFT-based estimators, we measure the power spectrum clustering wedges of the BOSS sample by filtering out the information of Legendre multipoles l > 4. Our modelling of these measurements is based on novel approaches to describe non-linear evolution, bias, and redshift-space distortions, which we test using synthetic catalogues based on large-volume N-body simulations. We are able to include smaller scales than in previous analyses, resulting in tighter cosmological constraints. Using three overlapping redshift bins, we measure the angular diameter distance, the Hubble parameter, and the cosmic growth rate, and explore the cosmological implications of our full shape clustering measurements in combination with CMB and SN Ia data. Assuming a ΛCDM cosmology, we constrain 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 (CL) of 68 per cent. We also allow for non-standard dark energy models and modifications of the growth rate, finding good agreement with the ΛCDM paradigm. For example, we constrain the equation-of-state parameter to w = -1.019 -0.039 +0.048. 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.

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The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Observational systematics and baryon acoustic oscillations in the correlation function

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.

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The XMM Cluster Survey: The Halo Occupation Number of BOSS galaxies in X-ray clusters

We present a direct measurement of the mean halo occupation distribution (HOD) of galaxies taken from the eleventh data release (DR11) of the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey (BOSS). The HOD of BOSS low-redshift (LOWZ: $0.2 < z < 0.4$) and Constant-Mass (CMASS: $0.43 <z <0.7$) galaxies is inferred via their association with the dark-matter halos of 174 X-ray-selected galaxy clusters drawn from the XMM Cluster Survey (XCS). Halo masses are determined for each galaxy cluster based on X-ray temperature measurements, and range between ${\rm log_{10}} (M_{180}/M_{\odot}) = 13-15$. Our directly measured HODs are consistent with the HOD-model fits inferred via the galaxy-clustering analyses of Parejko et al. for the BOSS LOWZ sample and White et al. for the BOSS CMASS sample. Under the simplifying assumption that the other parameters that describe the HOD hold the values measured by these authors, we have determined a best-fit alpha-index of 0.91$\pm$0.08 and $1.27^{+0.03}_{-0.04}$ for the CMASS and LOWZ HOD, respectively. These alpha-index values are consistent with those measured by White et al. and Parejko et al. In summary, our study provides independent support for the HOD models assumed during the development of the BOSS mock-galaxy catalogues that have subsequently been used to derive BOSS cosmological constraints.

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The Sloan Digital Sky Survey Quasar Catalog: twelfth data release

We present the Data Release 12 Quasar catalog (DR12Q) from the Baryon Oscillation Spectroscopic Survey (BOSS) of the SDSS-III. This catalog includes all SDSS-III/BOSS objects that were spectroscopically targeted as quasar candidates during the full survey and that are confirmed as quasars via visual inspection of the spectra, have luminosities Mi[z=2]<-20.5 (in a LCDM cosmology with H_0 = 70 km/s/Mpc, Omega_M = 0.3, and Omega _L=0.7), and either display at least one emission line with a full width at half maximum (FWHM)larger than 500 km/s or, if not, have interesting/complex absorption features. The catalog also includes previously known quasars (mostly from SDSS-I and II) that were reobserved by BOSS. The catalog contains 297,301 quasars detected over 9,376 square degrees with robust identification and redshift measured by a combination of principal component eigenspectra. The number of quasars with z>2.15 is about an order of magnitude greater than the number of z>2.15 quasars known prior to BOSS. Redshifts and FWHMs are provided for the strongest emission lines (CIV, CIII], MgII). The catalog identifies 29,580 broad absorption line quasars and lists their characteristics. For each object, the catalog presents five-band (u, g, r, i, z) CCD-based photometry together with some information on the optical morphology and the selection criteria. When available, the catalog also provides information on the optical variability of quasars using SDSS and PTF multi-epoch photometry. The catalog also contains X-ray, ultraviolet, near-infrared, and radio emission properties of the quasars, when available, from other large-area surveys. The calibrated digital spectra, covering the wavelength region 3,600-10,500A at a spectral resolution in the range 1,300<R<2,500, can be retrieved from the SDSS Catalog Archive Server.

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Galaxy Three-Point Correlation Functions and Halo/Subhalo Models

We present the measurements of the luminosity-dependent redshift-space three-point correlation functions (3PCFs) for the Sloan Digital Sky Survey (SDSS) DR7 Main galaxy sample. We compare the 3PCF measurements to the predictions from three different halo and subhalo models. One is the halo occupation distribution (HOD) model and the other two are extensions of the subhalo abundance matching (SHAM) model by allowing the central and satellite galaxies to have different occupation distributions in the host halos and subhalos. Parameters in all the models are chosen to best describe the projected and redshift-space two-point correlation functions (2PCFs) of the same set of galaxies. All three model predictions agree well with the 3PCF measurements for the most luminous galaxy sample, while the HOD model better performs in matching the 3PCFs of fainter samples (with luminosity threshold below $L^*$), which is similar in trend to the case of fitting the 2PCFs. The decomposition of the model 3PCFs into contributions from different types of galaxy triplets shows that on small scales the dependence of the 3PCFs on triangle shape is driven by nonlinear redshift-space distortion (and not by the intrinsic halo shape) while on large scales it reflects the filamentary structure. The decomposition also reveals more detailed differences in the three models, which are related to the radial distribution, the mean occupation function, and the velocity distribution of satellite galaxies inside halos. The results suggest that galaxy 3PCFs can further help constrain the above galaxy-halo relation and test theoretical models.

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Clustering properties of $g$-selected galaxies at $z\sim0.8$

Current and future large redshift surveys, as the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey (SDSS-IV/eBOSS) or the Dark Energy Spectroscopic Instrument (DESI), will use emission-line galaxies (ELG) to probe cosmological models by mapping the large-scale structure of the Universe in the redshift range $0.6 < z < 1.7$. With current data, we explore the halo-galaxy connection by measuring three clustering properties of $g$-selected ELGs as matter tracers in the redshift range $0.6 < z < 1$: (i) the redshift-space two-point correlation function using spectroscopic redshifts from the BOSS ELG sample and VIPERS; (ii) the angular two-point correlation function on the footprint of the CFHT-LS; (iii) the galaxy-galaxy lensing signal around the ELGs using the CFHTLenS. We interpret these observations by mapping them onto the latest high-resolution MultiDark Planck N-body simulation, using a novel (Sub)Halo-Abundance Matching technique that accounts for the ELG incompleteness. ELGs at $z\sim0.8$ live in halos of $(1\pm 0.5)\times10^{12}\,h^{-1}$M$_{\odot}$ and 22.5$\pm2.5$% of them are satellites belonging to a larger halo. The halo occupation distribution of ELGs indicates that we are sampling the galaxies in which stars form in the most efficient way, according to their stellar-to-halo mass ratio.

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The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: double-probe measurements from BOSS galaxy clustering \& Planck data -- towards an analysis without informative priors

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 $\{R$, $l_a$, $Ω_b h^2$, $n_s$, $log(A_s)$, $Ω_k$, $H(z)$, $D_A(z)$, $f(z)σ_8(z)\}$, which give an efficient summary of Planck data and 2-point statistics from BOSS galaxy sample, where $R=\sqrt{Ω_m H_0^2}\,r(z_*)$, and $l_a=πr(z_*)/r_s(z_*)$, $z_*$ 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. $Ω_b h^2$ and $n_s$. Using our double-probe results, we obtain $Ω_m=0.304\pm0.009$, $H_0=68.2\pm0.7$, and $σ_8=0.806\pm0.014$ assuming $Λ$CDM; and $Ω_k=0.002\pm0.003$ and $w=-1.00\pm0.07$ assuming o$w$CDM. The results show no tension with the flat $Λ$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 $Σm_ν<0.10/0.22$ (68\%/95\%) assuming $Λ$CDM and $Σm_ν<0.26/0.52$ (68\%/95\%) assuming $w$CDM. This paper is part of a set that analyses the final galaxy clustering dataset from BOSS.

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The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Baryon Acoustic Oscillations in Fourier-space

We analyse the Baryon Acoustic Oscillation (BAO) signal of the final Baryon Oscillation Spectroscopic Survey (BOSS) data release (DR12). Our analysis is performed in Fourier-space, using the power spectrum monopole and quadrupole. The dataset includes $1\,198\,006$ galaxies over the redshift range $0.2 < z < 0.75$. We divide this dataset into three (overlapping) redshift bins with the effective redshifts $\zeff = 0.38$, $0.51$ and $0.61$. We demonstrate the reliability of our analysis pipeline using N-body simulations as well as $\sim 1000$ MultiDark-Patchy mock catalogues, which mimic the BOSS-DR12 target selection. We apply density field reconstruction to enhance the BAO signal-to-noise ratio. By including the power spectrum quadrupole we can separate the line-of-sight and angular modes, which allows us to constrain the angular diameter distance $D_A(z)$ and the Hubble parameter $H(z)$ separately. We obtain two independent $1.6\%$ and $1.5\%$ constraints on $D_A(z)$ and $2.9\%$ and $2.3\%$ constraints on $H(z)$ for the low ($\zeff=0.38$) and high ($\zeff=0.61$) redshift bin, respectively. We obtain two independent $1\%$ and $0.9\%$ constraints on the angular averaged distance $D_V(z)$, 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 results are in good agreement with the Planck prediction within $Λ$CDM. 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~\citet{Alam2016} to produce the final cosmological constraints from BOSS.

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The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the configuration-space clustering wedges

We explore the cosmological implications of anisotropic clustering measurements in configuration space of the final galaxy samples from Data Release 12 of the SDSS-III Baryon Oscillation Spectroscopic Survey. We implement a new detailed modelling of the effects of non-linearities, galaxy bias and redshift-space distortions that can be used to extract unbiased cosmological information from our measurements for scales $s \gtrsim 20\,h^{-1}{\rm Mpc}$. We combined the galaxy clustering information from BOSS with the latest cosmic microwave background (CMB) observations and Type Ia supernovae samples and found no significant evidence for a deviation from the $Λ$CDM cosmological model. In particular, these data sets can constrain the dark energy equation of state parameter to $w_{\rm DE}=-0.996\pm0.042$ when assumed time-independent, the curvature of the Universe to $Ω_{k}=-0.0007\pm 0.0030$ and the sum of the neutrino masses to $\sum m_ν < 0.25\,{\rm eV}$ at 95 per cent CL. We explore the constraints on the growth rate of cosmic structures assuming $f(z)=Ω_{\rm m}(z)^γ$ and obtain $γ= 0.609\pm 0.079$, in good agreement with the predictions of general relativity of $γ=0.55$. We compress the information of our clustering measurements into constraints on the parameter combinations $D_{\rm V}(z)/r_{\rm d}$, $F_{\rm AP}(z)$ and $fσ_8(z)$ at the effective redshifts of $z=0.38$, $0.51$ and $0.61$ with their respective covariance matrices and find good agreement with the predictions for these parameters obtained from the best-fitting $Λ$CDM model to the CMB data from the Planck satellite. 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.

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