I present a new approach to recover the primordial density fluctuations and the cosmic web structure underlying a galaxy distribution. The method is based on sampling Gaussian fields which are ...compatible with a galaxy distribution and a structure formation model. This is achieved by splitting the inversion problem into two Gibbs-sampling steps: the first being a Gaussianization step transforming a distribution of point sources at Lagrangian positions - which are not a priori given- into a linear alias-free Gaussian field. This step is based on Hamiltonian sampling with a Gaussian-Poisson model. The second step consists on a likelihood comparison in which the set of matter tracers at the initial conditions is constrained on the galaxy distribution and the assumed structure formation model. For computational reasons second-order Lagrangian perturbation theory is used. However, the presented approach is flexible to adopt any structure formation model. A semi-analytic halo-model-based galaxy mock catalogue is taken to demonstrate that the recovered initial conditions are closely unbiased with respect to the actual ones from the corresponding N-body simulation down to scales of a ∼5 Mpc h
−1. The cross-correlation between them shows a substantial gain of information, being at k ∼ 0.3 h Mpc−1 more than doubled. In addition the initial conditions are extremely well Gaussian distributed and the power spectra follow the shape of the linear power spectrum being very close to the actual one from the simulation down to scales of k ∼ 1 h Mpc−1.
In this work we investigate the generation of mock halo catalogues based on perturbation theory and non-linear stochastic biasing with the novel patchy code. In particular, we use Augmented ...Lagrangian Perturbation Theory (ALPT) to generate a dark matter density field on a mesh starting from Gaussian fluctuations and to compute the peculiar velocity field. ALPT is based on a combination of second order LPT (2LPT) on large scales and the spherical collapse model on smaller scales. We account for the systematic deviation of perturbative approaches from N-body simulations together with halo biasing adopting an exponential bias model. We then account for stochastic biasing by defining three regimes: a low-, an intermediate- and a high-density regime, using a Poisson distribution in the intermediate regime and the negative binomial distribution - including an additional parameter - to model over-dispersion in the high-density regime. Since we focus in this study on massive haloes, we suppress the generation of haloes in the low-density regime. The various non-linear and stochastic biasing parameters, and density thresholds, are calibrated with the large BigMultiDark N-body simulation to match the power spectrum of the corresponding halo population. Our model effectively includes only five parameters, as they are additionally constrained by the halo number density. Our mock catalogues show power spectra, in both real- and redshift-space, which are compatible with N-body simulations within about 2 per cent up to k ∼ 1 h Mpc−1 at z = 0.577 for a sample of haloes with the typical Baryon Oscillation Spectroscopic Survey (BOSS) CMASS (constant stellar mass galaxy sample) galaxy number density. The corresponding correlation functions are compatible down to a few Mpc. We also find that neglecting over-dispersion in high-density regions produces power spectra with deviations of 10 per cent at k ∼ 0.4 h Mpc−1. These results indicate the need to account for an accurate statistical description of the galaxy clustering for precise studies of large-scale surveys.
Abstract We present a new fast and efficient approach to model structure formation with augmented Lagrangian perturbation theory (ALPT). Our method is based on splitting the displacement field into a ...long- and a short-range component. The long-range component is computed by second-order LPT (2LPT). This approximation contains a tidal non-local and non-linear term. Unfortunately, 2LPT fails on small scales due to severe shell crossing and a crude quadratic behaviour in the low-density regime. The spherical collapse (SC) approximation has been recently reported to correct for both effects by adding an ideal collapse truncation. However, this approach fails to reproduce the structures on large scales where it is significantly less correlated with the N-body result than 2LPT or linear LPT (the Zel'dovich approximation). We propose to combine both approximations using for the short-range displacement field the SC solution. A Gaussian filter with a smoothing radius rS is used to separate between both regimes. We use the result of 25 dark-matter-only N-body simulations to benchmark at z = 0 the different approximations: first-, second-, third-order LPT, SC and our novel combined ALPT model. This comparison demonstrates that our method improves previous approximations at all scales showing ∼25 and ∼75 per cent higher correlation than 2LPT with the N-body solution at k = 1 and 2 h Mpc−1, respectively. We conduct a parameter study to determine the optimal range of smoothing radii and find that the maximum correlation is achieved with rS = 4–5 h−1 Mpc. This structure formation approach could be used for various purposes, such as setting-up initial conditions for N-body simulations, generating mock galaxy catalogues, cosmic web analysis or for reconstructions of the primordial density fluctuations.
We measure and analyse the bispectrum of the final data release 12 (DR12), galaxy sample provided by the Baryon Oscillation Spectroscopic Survey, splitting by selection algorithm into LOWZ and CMASS ...galaxies. The LOWZ sample contains 361 762 galaxies with an effective redshift of z sub( LOWZ) = 0.32, and the CMASS sample contains 777 202 galaxies with an effective redshift of z sub( CMASS) = 0.57. Combining the power spectrum, measured relative to the line of sight, with the spherically averaged bispectrum, we are able to constrain the product of the growth of structure parameter, f, and the amplitude of dark matter density fluctuations, ..., along with the geometric Alcock-Paczynski parameters, the product of the Hubble constant and the comoving sound horizon at the baryon drag epoch, H(z)r sub( s)(z sub( d)), and the angular distance parameter divided by the sound horizon, D sub( A)(z)/r sub( s)(z sub( d)). After combining pre-reconstruction RSD analyses of the power spectrum monopole, quadrupole and bispectrum monopole with post-reconstruction analysis of the BAO power spectrum monopole and quadrupole, we find f(z sub( LOWZ))...(z sub( LOWZ)) = 0.427 plus or minus 0.056, D sub( A)(z sub( LOWZ))/r sub( s)(z sub( d)) = 6.60 plus or minus 0.13, H(z sub( LOWZ))r sub( s)(z sub( d)) = (11.55 plus or minus 0.38)10 super( 3) km s super( -1) for the LOWZ sample, and f(z sub( CMASS))...(z sub( CMASS)) = 0.426 plus or minus 0.029, D sub( A)(z sub( CMASS))/r sub( s)(z sub( d)) = 9.39 plus or minus 0.10, H(z sub( CMASS))r sub( s)(z sub( d)) = (14.02 plus or minus 0.22)10 super( 3) km s super( -1) for the CMASS sample. We find general agreement with previous Baryon Oscillation Spectroscopic Survey DR11 and DR12 measurements. Combining our data set with Planck15 we perform a null test of General Relativity through the ...-parametrization finding ...=0.733..., which is ~2.7... away from the General Relativity predictions. (ProQuest: ... denotes formulae/symbols omitted.)
We present an anisotropic analysis of the baryon acoustic oscillation (BAO) scale in the twelfth and final data release of the Baryon Oscillation Spectroscopic Survey (BOSS). We independently analyse ...the LOWZ and CMASS galaxy samples: the LOWZ sample contains 361 762 galaxies with an effective redshift of z
LOWZ = 0.32; the CMASS sample consists of 777 202 galaxies with an effective redshift of z
CMASS = 0.57. We extract the BAO peak position from the monopole power-spectrum moment, α0, and from the μ2 moment, α2, where μ is the cosine of the angle to the line of sight. The μ2-moment provides equivalent information to that available in the quadrupole but is simpler to analyse. After applying a reconstruction algorithm to reduce the BAO suppression by bulk motions, we measure the BAO peak position in the monopole and μ2-moment, which are related to radial and angular shifts in scale. We report H(z
LOWZ)r
s(z
d) = (11.60 ± 0.60) × 103 km s−1 and D
A(z
LOWZ)/r
s(z
d) = 6.66 ± 0.16 with a cross-correlation coefficient of
$r_{HD_{\rm A}}=0.41$
, for the LOWZ sample; and H(z
CMASS)r
s(z
d) = (14.56 ± 0.37) × 103 km s−1 and D
A(z
CMASS)/r
s(z
d) = 9.42 ± 0.13 with a cross-correlation coefficient of
$r_{HD_{\rm A}}=0.47$
, for the CMASS sample. We demonstrate that our results are not affected by the fiducial cosmology assumed for the analysis. We combine these results with the measurements of the BAO peak position in the monopole and quadrupole correlation function of the same data set (Cuesta et al. 2016, companion paper) and report the consensus values: H(z
LOWZ)r
s(z
d) = (11.63 ± 0.69) × 103 km s−1 and D
A(z
LOWZ)/r
s(z
d) = 6.67 ± 0.15 with
$r_{HD_{\rm A}}=0.35$
for the LOWZ sample; H(z
CMASS)r
s(z
d) = (14.67 ± 0.42) × 103 km s−1 and D
A(z
CMASS)/r
s(z
d) = 9.47 ± 0.12 with
$r_{HD_{\rm A}}=0.52$
for the CMASS sample.
We present a new methodology to generate mock halo or galaxy catalogues, which have accurate clustering properties, nearly indistinguishable from full N-body solutions, in terms of the one-point, ...two-point, and three-point statistics. In particular, the agreement is remarkable, within 1 per cent up to k = 0.55 h Mpc... and down to r = 10 h... Mpc, for the power spectrum and two-point correlation function, respectively, while the bispectrum agrees in general within 20 per cent for different scales and shapes. Our approach is based on the Zel'dovich approximation, however, effectively including with the simple prescriptions the missing physical ingredients, and stochastic scale-dependent, non-local, and non-linear biasing contributions. The computing time and memory required to produce one mock is similar to that using the lognormal model. With high accuracy and efficiency, the effective Zel'dovich approximation mocks (EZmocks) provide a reliable and practical method to produce massive mock galaxy catalogues for the analysis of large-scale structure measurements. (ProQuest: ... denotes formulae/symbols omitted.)
We measure and analyse the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) relative to the line of sight (LOS), for LOWZ and CMASS galaxy samples drawn from the final Data Release ...12. The LOWZ sample contains 361 762 galaxies with an effective redshift of z
lowz = 0.32, and the CMASS sample 777 202 galaxies with an effective redshift of z
cmass = 0.57. From the power spectrum monopole and quadrupole moments around the LOS, we measure the growth of structure parameter f times the amplitude of dark matter density fluctuations σ8 by modelling the redshift-space distortion signal. When the geometrical Alcock–Paczynski effect is also constrained from the same data, we find joint constraints on fσ8, the product of the Hubble constant and the comoving sound horizon at the baryon-drag epoch H(z)r
s(z
d), and the angular distance parameter divided by the sound horizon D
A(z)/r
s(z
d). We find f(z
lowz)σ8(z
lowz) = 0.394 ± 0.062, D
A(z
lowz)/r
s(z
d) = 6.35 ± 0.19, H(z
lowz)r
s(z
d) = (11.41 ± 0.56) 103 km s− 1 for the LOWZ sample, and f(z
cmass)σ8(z
cmass) = 0.444 ± 0.038, D
A(z
cmass)/r
s(z
d) = 9.42 ± 0.15, H(z
cmass)r
s(z
d) = (13.92 ± 0.44) 103 km s− 1 for the CMASS sample. We find general agreement with previous BOSS DR11 measurements. Assuming the Hubble parameter and angular distance parameter are fixed at fiducial Λcold dark matter values, we find f(z
lowz)σ8(z
lowz) = 0.485 ± 0.044 and f(z
cmass)σ8(z
cmass) = 0.436 ± 0.022 for the LOWZ and CMASS samples, respectively.
We investigate the anisotropic clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12 sample, which consists of 1198 006 galaxies in the redshift range 0.2 < z < 0.75 and a ...sky coverage of 10 252 deg2. We analyse this data set in Fourier space, using the power-spectrum multipoles to measure redshift-space distortions simultaneously with the Alcock-Paczynski effect and the baryon acoustic oscillation scale. We include the power-spectrum monopole, quadrupole and hexadecapole in our analysis and compare our measurements with a perturbation-theory-based model, while properly accounting for the survey window function. To evaluate the reliability of our analysis pipeline, we participate in a mock challenge, which results in systematic uncertainties significantly smaller than the statistical uncertainties. While the high-redshift constraint on fs8 at zeff = 0.61 indicates a small (~1.4s) deviation from the prediction of the Planck ...CDM (... cold dark matter) model, the low-redshift constraint is in good agreement with Planck ...CDM. This paper is part of a set that analyses the final galaxy clustering data set from BOSS. The measurements and likelihoods presented here are combined with others in Alam et al. to produce the final cosmological constraints from BOSS. (ProQuest: ... denotes formulae/symbols omitted.)
Abstract
We report a measurement of the large-scale three-point correlation function of galaxies using the largest data set for this purpose to date, 777 202 luminous red galaxies in the Sloan ...Digital Sky Survey Baryon Acoustic Oscillation Spectroscopic Survey (SDSS BOSS) DR12 CMASS sample. This work exploits the novel algorithm of Slepian & Eisenstein to compute the multipole moments of the 3PCF in
$\mathcal {O}(N^2)$
time, with N the number of galaxies. Leading-order perturbation theory models the data well in a compressed basis where one triangle side is integrated out. We also present an accurate and computationally efficient means of estimating the covariance matrix. With these techniques, the redshift-space linear and non-linear bias are measured, with 2.6 per cent precision on the former if σ8 is fixed. The data also indicate a 2.8σ preference for the BAO, confirming the presence of BAO in the three-point function.
Abstract
We perform a tomographic baryon acoustic oscillations (BAOs) analysis using the two-point galaxy correlation function measured from the combined sample of Baryon Oscillation Spectroscopic ...Survey Data Release 12 (BOSS DR12), which covers the redshift range of 0.2 < z < 0.75. Upon splitting the sample into multiple overlapping redshift slices to extract the redshift information of galaxy clustering, we obtain a measurement of DA
(z)/rd
and H(z)rd
at nine effective redshifts with the full covariance matrix calibrated using MultiDark-Patchy mock catalogues. Using the reconstructed galaxy catalogues, we obtain the precision of 1.3–2.2 per cent for DA
(z)/rd
and 2.1–6.0 per cent for H(z)rd
. To quantify the gain from the tomographic information, we compare the constraints on the cosmological parameters using our nine-bin BAO measurements, the consensus three-bin BAO and redshift space distortion measurements at three effective redshifts in Alam et al., and the non-tomographic (one-bin) BAO measurement at a single effective redshift. Comparing the nine-bin with one-bin constraint result, it can improve the dark energy Figure of Merit by a factor of 1.24 for the Chevallier–Polarski–Linder parametrization for equation-of-state parameter w
DE. The errors of w
0 and wa
from nine-bin constraints are slightly improved when compared to the three-bin constraint result.
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