Reconstructed Density Field Research Articles

Analysis of an iterative reconstruction method in comparison of the standard reconstruction method

ABSTRACT We present a detailed analysis of a new iterative density reconstruction algorithm. This algorithm uses a decreasing smoothing scale to better reconstruct the density field in Lagrangian space. We implement this algorithm to run on the quijote simulations, and extend it to (a) include a smoothing kernel that smoothly goes from anisotropic to isotropic, and (b) a variant that does not correct for redshift space distortions. We compare the performance of this algorithm with the standard reconstruction method. Our examinations of the methods include cross-correlation of the reconstructed density field with the linear density field, reconstructed two-point functions, and BAO parameter fitting. We also examine the impact of various parameters, such as smoothing scale, anisotropic smoothing, tracer type/bias, and the inclusion of second order perturbation theory. We find that the two reconstruction algorithms are comparable in most of the areas we examine. In particular, both algorithms give consistent fittings of BAO parameters. The fits are robust over a range of smoothing scales. We find the iterative algorithm is significantly better at removing redshift space distortions. The new algorithm will be a promising method to be employed in the ongoing and future large-scale structure surveys.

Neural network reconstruction of density and velocity fields from the 2MASS Redshift Survey

Aims. Our aim is to reconstruct the 3D matter density and peculiar velocity fields in the local Universe up to a distance of 200 h−1 Mpc from the Two-Micron All-Sky Redshift Survey (2MRS) using a neural network (NN). Methods. We employed an NN with a U-net autoencoder architecture and a weighted mean squared error loss function trained separately to output either the density or velocity field for a given input grid of galaxy number counts. The NN was trained on mocks derived from the Quijote N-body simulations, incorporating redshift-space distortions (RSDs), galaxy bias, and selection effects closely mimicking the characteristics of 2MRS. The trained NN was benchmarked against a standard Wiener filter (WF) on a validation set of mocks before applying it to 2MRS. Results. The NN reconstructions effectively approximate the mean posterior estimate of the true density and velocity fields conditioned on the observations. They consistently outperform the WF in terms of reconstruction accuracy and effectively capture the nonlinear relation between velocity and density. The NN-reconstructed bulk flow of the total survey volume exhibits a significant correlation with the true mock bulk flow, demonstrating that the NN is sensitive to information on “super-survey” scales encoded in the RSDs. When applied to 2MRS, the NN successfully recovers the main known clusters, some of which are partially in the Zone of Avoidance. The reconstructed bulk flows in spheres of different radii less than 100 h−1 Mpc are in good agreement with a previous 2MRS analysis that required an additional external bulk flow component inferred from directly observed peculiar velocities. The NN-reconstructed peculiar velocity of the Local Group closely matches the observed Cosmic Microwave Background dipole in amplitude and Galactic latitude, and only deviates by 18° in longitude. The NN-reconstructed fields are publicly available.

Emulating Power Spectra for Prereconstructed and Postreconstructed Galaxy Samples

The small-scale linear information in galaxy samples typically lost during nonlinear growth can be restored to a certain level by the density field reconstruction, which has been demonstrated for improving the precision of the baryon acoustic oscillation (BAO) measurements. As proposed in the literature, a joint analysis of the power spectrum before and after the reconstruction enables an efficient extraction of information carried by high-order statistics. However, the statistics of the postreconstruction density field are difficult to model. In this work, we circumvent this issue by developing an accurate emulator for the prereconstructed, postreconstructed, and cross-power spectra ( Ppre , P post, P cross) up to k = 0.5 h Mpc−1 based on the Dark Quest N-body simulations. The accuracy of the emulator is at the percent level; namely, the error of the emulated monopole and quadrupole of the power spectra is less than 1% and 10% of the ground truth, respectively. A fit to an example power spectrum using the emulator shows that the constraints on cosmological parameters get largely improved using Ppre +P post+P cross with kmax=0.25hMpc−1 , compared to that derived from Ppre alone; namely, the constraints on (Ω m , H 0, σ 8) are tightened by ∼41%–55%, and the uncertainties of the derived BAO and RSD parameters (α ⊥, α ∣∣, f σ 8) shrink by ∼28%–54%, respectively. This highlights the complementarity among Ppre , P post, and P cross, which demonstrates the efficiency and practicability of a joint Ppre , P post, and P cross analysis for cosmological implications.

Extracting high-order cosmological information in galaxy surveys with power spectra

The reconstruction method was proposed more than a decade ago to boost the signal of baryonic acoustic oscillations measured in galaxy redshift surveys, which is one of key probes for dark energy. After moving the observed overdensities in galaxy surveys back to their initial position, the reconstructed density field is closer to a linear Gaussian field, with higher-order information moved back into the power spectrum. We find that by jointly analysing power spectra measured from the pre- and post-reconstructed galaxy samples, higher-order information beyond the 2-point power spectrum can be efficiently extracted, which generally yields an information gain upon the analysis using the pre- or post-reconstructed galaxy sample alone. This opens a window to easily use higher-order information when constraining cosmological models.

Evaluate Geometry of Radiance Fields with Low-Frequency Color Prior

A radiance field is an effective representation of 3D scenes, which has been widely adopted in novel-view synthesis and 3D reconstruction. It is still an open and challenging problem to evaluate the geometry, i.e., the density field, as the ground-truth is almost impossible to obtain. One alternative indirect solution is to transform the density field into a point-cloud and compute its Chamfer Distance with the scanned ground-truth. However, many widely-used datasets have no point-cloud ground-truth since the scanning process along with the equipment is expensive and complicated. To this end, we propose a novel metric, named Inverse Mean Residual Color (IMRC), which can evaluate the geometry only with the observation images. Our key insight is that the better the geometry, the lower-frequency the computed color field. From this insight, given a reconstructed density field and observation images, we design a closed-form method to approximate the color field with low-frequency spherical harmonics, and compute the inverse mean residual color. Then the higher the IMRC, the better the geometry. Qualitative and quantitative experimental results verify the effectiveness of our proposed IMRC metric. We also benchmark several state-of-the-art methods using IMRC to promote future related research. Our code is available at https://github.com/qihangGH/IMRC.

Subsoil density field reconstruction through 3-D FWI: a systematic comparison between vertical- and horizontal-force seismic sources

SUMMARY Bulk-density (ρ) of soil is an important indicator of soil compaction and type. A knowledge of the spatial variability of in situ soil density is important in geotechnical engineering, hydrology and agriculture. Surface geophysical methods have so far shown limited success in providing an accurate and high-resolution image of 3-D soil-density distribution. In this pursuit, 3-D seismic full-waveform inversion (FWI) is promising, provided the robustness and accuracy of density inversion via this approach can be established in the near-surface scale. However, simultaneous reconstruction of ρ and seismic wave velocities through multiparameter FWI remains a challenging task. Near-surface seismic data are commonly dominated by dispersive surface waves whose velocities are controlled by the value and distribution of shear-wave velocity (VS). One major difficulty in estimating reliably ρ from near-surface seismic data is due to the relatively low sensitivity of the seismic wavefield to ρ compared to seismic velocities. Additionally, the accuracy of the estimated ρ decreases due to error in VS—an issue known as parameter coupling. Parameter coupling makes it difficult to estimate accurately ρ within the framework of conventional gradient-based FWI. More sophisticated optimization approaches (e.g. truncated Newton) can reduce the effect of parameter coupling, but these approaches are commonly not affordable in near-surface applications due to heavy computational burden. In this research, we have investigated how choosing correctly the force direction of the seismic source can contribute to a higher accuracy of ρ estimates through 3-D FWI. Using scattered wavefields, the Hessian, and inversion tests, an in-depth and systematic investigation of data sets corresponding to different force directions has been carried out. A comparison of the scattered wavefields due to a point-localized ρ perturbation for different force directions shows the robustness of the horizontal-force data set to noise compared to the vertical-force data set. Furthermore, for a point-scatterer model, an analysis of the gradients of the misfit function using the Hessian shows that utilizing a horizontal-force source enables one to reconstruct the high-resolution gradient with relatively small parameter coupling. Finally, inversion tests for two different subsoil models demonstrate that 3-D FWI on a horizontal-force-source seismic data set is capable of providing a more accurate 3-D ρ distribution in soil compared to a vertical-force-source data set. Our results show that the use of a horizontal-force source might allow avoiding computationally demanding, costly optimization approaches in 3-D FWI.

Reconstruction Method of 3D Turbulent Flames by Background-Oriented Schlieren Tomography and Analysis of Time Asynchrony

Background-oriented Schlieren tomography (BOST) is widely used for 3D reconstruction of turbulent flames. Two major concerns are associated with 3D reconstruction. One is the time asynchrony within the data acquisition of the high-speed camera. The other is that the ray tracing process requires significant computational consumption. This study proposes a ray tracing optimization method based on the k-d tree. The study results show that the average search nodes for each ray are only 0.018% of 3D flame with 3.07 million grid nodes. In addition, a parameter estimation method of the unknown azimuth power spectrum function is proposed. First, a typical Sandia turbulent jet diffusion flame dataset was built and validated accordingly, with experiments. The algorithm’s applicability to the 3D reconstruction of temperature and density fields is discussed on this basis. The root-mean-square error (RMSE) of the cross-section density for 3D reconstruction is below 0.1 kg/m3. In addition, the RMSE of the cross-section temperature is below 270 K. Finally, an uncertainty analysis of the flame reconstruction based on a physical model is performed by optimizing the ray tracing method. For the time asynchronous variance of 1 ms, the density uncertainty of the 3D reconstruction is below 1.6 × 10−2 kg/m3, and the temperature uncertainty is below 70 K. The method can provide an essential basis for the design of BOST systems and the 3D reconstruction of turbulent flames.

Effective cosmic density field reconstruction with convolutional neural network

ABSTRACT We present a cosmic density field reconstruction method that augments the traditional reconstruction algorithms with a convolutional neural network (CNN). Following previous work, the key component of our method is to use the reconstructed density field as the input to the neural network. We extend this previous work by exploring how the performance of these reconstruction ideas depends on the input reconstruction algorithm, the reconstruction parameters, and the shot noise of the density field, as well as the robustness of the method. We build an eight-layer CNN and train the network with reconstructed density fields computed from the Quijote suite of simulations. The reconstructed density fields are generated by both the standard algorithm and a new iterative algorithm. In real space at z = 0, we find that the reconstructed field is 90 per cent correlated with the true initial density out to $k\sim 0.5 \, \mathrm{ h}\, \rm {Mpc}^{-1}$, a significant improvement over $k\sim 0.2 \, \mathrm{ h}\, \rm {Mpc}^{-1}$ achieved by the input reconstruction algorithms. We find similar improvements in redshift space, including an improved removal of redshift space distortions at small scales. We also find that the method is robust across changes in cosmology. Additionally, the CNN removes much of the variance from the choice of different reconstruction algorithms and reconstruction parameters. However, the effectiveness decreases with increasing shot noise, suggesting that such an approach is best suited to high density samples. This work highlights the additional information in the density field beyond linear scales as well as the power of complementing traditional analysis approaches with machine learning techniques.

Quantitative Investigation of Ballistics Flow Fields by Background Oriented Schlieren Technique

The ballistics field is known by the presence of several complex phenomena such as muzzles and flying projectiles flow fields. Consequently, numerical simulations are commonly used to model these complicated flows. However, the validation process of these codes has proven to be problematic due to the lack of experimental quantitative data. In this context, the present paper describes the application of the Background Oriented Schlieren technique (BOS) as a quantitative investigation tool in the ballistics field. We illustrate that BOS can accurately capture the main characteristics of the studied configurations: Firstly, we discuss the visualization and the density field reconstruction around a Bullet Simulated Projectile BSP flying at supersonic velocities and a sniper projectile flying at supersonic and transonic velocities. We demonstrate that these fields are in satisfactory agreement with the results of Taylor and Maccoll’s equation and numerical simulation. Then, the findings of the BOS visualization of the precursors and the propellant flow fields are presented. To this end, the salient features accurately captured by the BOS technique such as vortex rings, shock bottles, Mach, and blast wave are described both qualitatively and in terms of density profiles. Two improved approaches that are essential to the aforementioned analysis are proposed: the first is related to density field reconstruction based on Abel inversion and the second approach is a phase separation procedure.

Large-scale density and velocity field reconstructions with neural networks

ABSTRACT We assess a neural network (NN) method for reconstructing 3D cosmological density and velocity fields (target) from discrete and incomplete galaxy distributions (input). We employ second-order Lagrangian Perturbation Theory to generate a large ensemble of mock data to train an auto-encoder (AE) architecture with a Mean Squared Error (MSE) loss function. The AE successfully captures non-linear features arising from gravitational dynamics and the discreteness of the galaxy distribution. It preserves the positivity of the reconstructed density field and exhibits a weaker suppression of the power on small scales than the traditional linear Wiener filter (WF), which we use as a benchmark. In the density reconstruction, the reduction of the AE MSE relative to the WF is $\sim 15~{{\ \rm per\ cent}}$ , whereas for the velocity reconstruction a relative reduction of up to a factor of two can be achieved. The AE is advantageous to the WF at recovering the distribution of the target fields, especially at the tails. In fact, trained with an MSE loss, any NN estimate approaches the unbiased mean of the underlying target given the input. This implies a slope of unity in the linear regression of the true on the NN-reconstructed field. Only for the special case of Gaussian fields, the NN and WF estimates are equivalent. Nonetheless, we also recover a linear regression slope of unity for the WF with non-Gaussian fields.

Tomographic Reconstruction of Water Vapor Density Fields From the Integration of GNSS Observations and Fengyun-4A Products

The potential of precipitable water vapor (PWV) maps retrieved by remote sensing satellites can address the geometry defect of global navigation satellite system (GNSS) observations in tropospheric tomography. The second-generation geostationary meteorological satellite Fengyun-4A (FY-4A) of China can provide PWV products with high spatial (4 km) and temporal (15 min) resolutions. This article presents the first study on water vapor tomography by integrating GNSS measurements and FY-4A products using the node-based parameterized method. Layer PWV (LPW) products of FY-4A instead of the total PWV are adopted, which can increase the rank of the tomographic equation significantly. The integrated tomography model is validated with observational data collected over the three-month period of June to August 2020 from 124 GNSS stations in Hunan province, China. Assessments using radiosonde and European Centre for Medium-Range Weather Forecasts ReAnalysis 5 (ERA5) data demonstrate the better performance of the integrated model against the traditional model using GNSS data alone. In the assessment with radiosonde profiles, the integrated model improves the tomographic solutions upon the traditional model by 40.58% and 36.33% for 30- and 15-min resolutions, respectively. Root mean square errors (RMSEs) of density differences between ERA5 and the integrated model vary from 1.24 to 2.82 g/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{3}$ </tex-math></inline-formula> throughout the study area. RMSEs vertically decrease from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 5$ </tex-math></inline-formula> g/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{3}$ </tex-math></inline-formula> at the bottom to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim 0.5$ </tex-math></inline-formula> g/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{3}$ </tex-math></inline-formula> at the top layer of about 10 km. This work demonstrates the benefit of high-quality FY-4A products to GNSS tomography because they can effectively mitigate the ill-posed problem of inverse process.

Constraining the Fluctuating Gunn–Peterson Approximation using Lyα Forest Tomography at z = 2

The fluctuating Gunn–Peterson approximation (FGPA) is a commonly used method to generate mock Lyα forest absorption skewers at Cosmic Noon (z ≳ 2) from the matter density field of N-body simulations without running expensive hydrodynamical simulations. Motivated by recent developments in 3D intergalactic medium (IGM) tomography observations as well as matter density field reconstruction techniques applied to galaxy redshift samples at z ∼ 2, we examine the possibility of observationally testing FGPA by directly examining the relationship between Lyα transmission and the underlying matter density field. Specifically, we analyze the EAGLE, Illustris, IllustrisTNG, and Nyx cosmological hydrodynamic simulations that were run with different codes and sub-grid models. While the FGPA is an excellent description of the IGM in lower-density regions, the slope of the transmission–density distribution at higher densities is significantly affected by feedback processes causing the FGPA to break down in that regime. Even without added feedback, we find significant deviations caused by hydrodynamical effects arising from nonlinear structure growth. We then proceed to make comparisons using realistic mock data assuming the sightline sampling and spectral properties of the recent CLAMATO survey, and find that it would be challenging to discern between the FGPA and hydrodynamical models with current data sets. However, the improved sightline sampling from future extremely large telescopes or large volumes from multiplexed spectroscopic surveys such as Subaru PFS should allow for stringent tests of the FGPA, and make it possible to detect the effect of galaxy feedback on the IGM.

Iterative reconstruction excursions for Baryon Acoustic Oscillations and beyond

ABSTRACT The density field reconstruction technique has been widely used for recovering the baryon acoustic oscillation (BAO) feature in galaxy surveys that has been degraded due to non-linearities. Recent studies advocated adopting iterative steps to improve the recovery much beyond that of the standard technique. In this paper, we investigate the performance of a few selected iterative reconstruction techniques focusing on the BAO and the broad-band shape of the two-point clustering. We include redshift-space distortions, halo bias, and shot noise and inspect the components of the reconstructed field in Fourier space and in configuration space using both density field-based reconstruction and displacement field-based reconstruction. We find that the displacement field reconstruction becomes quickly challenging in the presence of non-negligible shot noise and therefore present surrogate methods that can be practically applied to a much more sparse field such as galaxies. For a galaxy field, implementing a debiasing step to remove the Lagrangian bias appears crucial for the displacement field reconstruction. We show that the iterative reconstruction does not substantially improve the BAO feature beyond an aggressively optimized standard reconstruction with a small smoothing kernel. However, we find taking iterative steps allows us to use a small smoothing kernel more ‘stably’, i.e. without causing a substantial deviation from the linear power spectrum on large scales. In one specific example we studied, we find that a deviation of 13 per cent in $P(k\sim 0.1\, h{\rm \,\,Mpc^{-1}})$ with an aggressive standard reconstruction can reduce to 3–4 per cent with iterative steps.

Constraints on equivalence principle violation from gamma ray bursts

Theories of gravity that obey the Weak Equivalence Principle have the same Parametrised Post-Newtonian parameter $\gamma$ for all particles at all energies. The large Shapiro time delays of extragalactic sources allow us to put tight constraints on differences in $\gamma$ between photons of different frequencies from spectral lag data, since a non-zero $\Delta \gamma$ would result in a frequency-dependent arrival time. The majority of previous constraints have assumed that the Shapiro time delay is dominated by a few local massive objects, although this is a poor approximation for distant sources. In this work we consider the cosmological context of these sources by developing a source-by-source, Monte Carlo-based forward model for the Shapiro time delays by combining constrained realisations of the local density field using the Bayesian origin reconstruction from galaxies algorithm with unconstrained large-scale modes. Propagating uncertainties in the density field reconstruction and marginalising over an empirical model describing other contributions to the time delay, we use spectral lag data of Gamma Ray Bursts from the BATSE satellite to constrain $\Delta \gamma < 2.1 \times 10^{-15}$ at $1 \sigma$ confidence between photon energies of $25 {\rm \, keV}$ and $325 {\rm \, keV}$.

Laguerre reconstruction of the BAO feature in halo-based mock galaxy catalogues

Fitting half-integer generalized Laguerre functions to the evolved, real-space dark matter and halo correlation functions provides a simple way to reconstruct their initial shapes. We show that this methodology also works well in a wide variety of realistic, assembly biased, velocity biased and redshift-space distorted mock galaxy catalogs. We use the linear point feature in the monopole of the redshift-space distorted correlation function to quantify the accuracy of our approach. We find that the linear point estimated from the mock galaxy catalogs is insensitive to the details of the biasing scheme at the subpercent level. However, the linear point scale in the nonlinear, biased, and redshift-space distorted field is systematically offset from its scale in the unbiased linear density fluctuation field by more than 1%. In the Laguerre reconstructed correlation function, this is reduced to sub-percent values, so it provides comparable accuracy and precision to methods that reconstruct the full density field before estimating the distance scale. The linear point in the reconstructed density fields provided by these other methods is likewise precise, accurate, and insensitive to galaxy bias. All reconstructions depend on some input parameters, and marginalizing over uncertainties in the input parameters required for reconstruction can degrade both accuracy and precision. The linear point simplifies the marginalization process, enabling more realistic estimates of the precision of the distance scale estimate for negligible additional computational cost. We show this explicitly for Laguerre reconstruction.

Beyond Taylor\u2019s hypothesis: a novel volumetric reconstruction of velocity and density fields for variable\u2011density and shear flows

This work presents a novel numerical procedure for reconstructing volumetric density and velocity fields from planar laser-induced fluorescence (PLIF) and stereoscopic particle image velocimetry (SPIV) data. This new method is theoretically and practically demonstrated to provide more accurate 3D vortical structures and density fields in high shear flows than reconstruction methods based on the mean convective velocity. While Taylor’s hypothesis of frozen turbulence is commonly applied by using the local mean streamwise velocity, the proposed algorithm uses the measured local instantaneous velocity for data convection. It consists of a step-by-step reconstruction based on a mixed Lagrangian–Eulerian solver that includes the 3D interpolation of scattered flow data and that relaxes the Taylor’s hypothesis by iterative enforcement of the incompressibility constraint on the velocity field. This methodology provides 3D fields with temporal resolution, spatial resolution, and accuracy comparable to that of real 3D snapshots, thus providing a practical alternative to tomographic measurements. The procedure is validated using numerical data of the constant-density channel flow available on the Johns Hopkins University Turbulence Database (JHTDB), showing the accurate reconstruction of the 3D velocity field. The algorithm is applied to an experimental dataset of PLIF and SPIV measurements of a variable-density jet flow, demonstrating its capability to provide 3D velocity and density fields that are more consistent with the Navier–Stokes equations compared to the mean flow convective method.Graphic abstract

Smooth stochastic density field reconstruction

ABSTRACT We introduce a method for generating a continuous, mass-conserving and high-order differentiable density field from a discrete point distribution such as particles or haloes from an N-body simulation or galaxies from a spectroscopic survey. The method consists on generating an ensemble of point realizations by perturbing the original point set following the geometric constraints imposed by the Delaunay tessellation in the vicinity of each point in the set. By computing the mean field of the ensemble we are able to significantly reduce artefacts arising from the Delaunay tessellation in poorly sampled regions while conserving the features in the point distribution. Our implementation is based on the Delaunay Tessellation Field Estimation (DTFE) method; however, other tessellation techniques are possible. The method presented here shares the same advantages of the DTFE method such as self-adaptive scale, mass conservation, and continuity, while being able to reconstruct even the faintest structures of the point distribution usually dominated by artefacts in Delaunay-based methods. Additionally, we also present preliminary results of an application of this method to image denoising and artefact removal, highlighting the broad applicability of the technique introduced here.

Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

Towards a self-consistent analysis of the anisotropic galaxy two- and three-point correlation functions on large scales: application to mock galaxy catalogues

ABSTRACT We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF, respectively) on the basis of the decomposition formalism of the 3PCF using tripolar spherical harmonics. We perform such an analysis with MultiDark-Patchy mock catalogues to demonstrate and understand the benefit of the anisotropic 3PCF. We focus on scales above $80\, h^{-1}\, {\rm Mpc}$, and use information from the shape and the baryon acoustic oscillation (BAO) signals of the 2PCF and 3PCF. We also apply density field reconstruction to increase the signal-to-noise ratio of BAO in the 2PCF measurement, but not in the 3PCF measurement. In particular, we study in detail the constraints on the angular diameter distance and the Hubble parameter. We build a model of the bispectrum or 3PCF that includes the non-linear damping of the BAO signal in redshift space. We carefully account for various uncertainties in our analysis including theoretical models of the 3PCF, window function corrections, biases in estimated parameters from the fiducial values, the number of mock realizations to estimate the covariance matrix, and bin size. The joint analysis of the 2PCF and 3PCF monopole and quadrupole components shows a $30{{\ \rm per\ cent}}$ and $20{{\ \rm per\ cent}}$ improvement in Hubble parameter constraints before and after reconstruction of the 2PCF measurements, respectively, compared to the 2PCF analysis alone. This study clearly shows that the anisotropic 3PCF increases cosmological information from galaxy surveys and encourages further development of the modelling of the 3PCF on smaller scales than we consider.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: large-scale structure catalogues and measurement of the isotropic BAO between redshift 0.6 and 1.1 for the Emission Line Galaxy Sample

ABSTRACT We present the Emission Line Galaxy (ELG) sample of the extended Baryon Oscillation Spectroscopic Survey from the Sloan Digital Sky Survey IV Data Release 16. We describe the observations and redshift measurement for the 269 243 observed ELG spectra, and then present the large-scale structure catalogues, used for the cosmological analysis, and made of 173 736 reliable spectroscopic redshifts between 0.6 and 1.1. We perform a spherically averaged baryon acoustic oscillations (BAO) measurement in configuration space, with density field reconstruction: the data two-point correlation function shows a feature consistent with that of the BAO, the BAO model being only weakly preferred over a model without BAO (Δχ2 &amp;lt; 1). Fitting a model constrained to have a BAO feature provides a 3.2 per cent measurement of the spherically averaged BAO distance DV(zeff)/rdrag = 18.23 ± 0.58 at the effective redshift zeff = 0.845.