Cosmic Density Field Research Articles

Filaments of the Slime Mold Cosmic Web and How They Affect Galaxy Evolution

We present a novel approach for identifying cosmic web filaments within the DisPerSE structure identification framework, using cosmic density field estimates from the Monte Carlo Physarum Machine (MCPM), inspired by the slime mold organism. We apply our method to the IllustrisTNG (TNG100) cosmological simulations and investigate the impact of filaments on galaxies. The MCPM density field is superior to the Delaunay tessellation field estimator in tracing the true underlying matter distribution and allows filaments to be identified with higher fidelity, finding more low-prominence/diffuse filaments. Using our new filament catalogs, we find that ≳90% of galaxies are located within ∼1.5 Mpc of a filamentary spine, with little change in the median star formation activity with distance to the nearest filament. Instead, we uncover a differential effect of the local filament line density, Σfil (MCPM)—the total MCPM overdensity per unit length along a filament segment—on galaxy formation: most galaxies are quenched and gas-poor near high-line density filaments at z ≤ 1. At earlier times, the filamentary environment appears to have no effect on galactic gas supply and quenching. At z = 0, quenching in log(M*/M⊙)≳10.5 galaxies is mainly driven by mass, while lower-mass galaxies are significantly affected by the filament line density. Satellites are far more susceptible to filaments than centrals. The local environments of massive halos are not sufficient to account for the effect of filament line density on gas removal and quenching. Our new approach holds great promise for observationally identifying filaments from galaxy surveys such as SDSS and DESI.

Beyond 3×2-point cosmology: the integrated shear and galaxy 3-point correlation functions

We present the integrated 3-point correlation functions (3PCF) involving both the cosmic shear and the galaxy density fields. These are a set of higher-order statistics that describe the modulation of local 2-point correlation functions (2PCF) by large-scale features in the fields, and which are easy to measure from galaxy imaging surveys. Based on previous works on the shear-only integrated 3PCF, we develop the theoretical framework for modelling 5 new statistics involving the galaxy field and its cross-correlations with cosmic shear. Using realistic galaxy and cosmic shear mocks from simulations, we determine the regime of validity of our models based on leading-order standard perturbation theory with an MCMC analysis that recovers unbiased constraints of the amplitude of fluctuations parameter A s and the linear and quadratic galaxy bias parameters b 1 and b 2. Using Fisher matrix forecasts for a DES-Y3-like survey, relative to baseline analyses with conventional 3×2PCFs, we find that the addition of the shear-only integrated 3PCF can improve cosmological parameter constraints by 20–40%. The subsequent addition of the new statistics introduced in this paper can lead to further improvements of 10–20%, even when utilizing only conservatively large scales where the tree-level models are valid. Our results motivate future work on the galaxy and shear integrated 3PCFs, which offer a practical way to extend standard analyses based on 3×2PCFs to systematically probe the non-Gaussian information content of cosmic density fields.

Statistics of tidal and deformation eigenvalue fields in the primordial Gaussian matter distribution: the two-dimensional case

ABSTRACT We study the statistical properties of the eigenvalues of the primordial tidal and deformation tensor for two-dimensional random Gaussian cosmic density fields. With the tidal and deformation tensors, Hessians of the gravitational and velocity potential, being Gaussian, the eigenvalue fields are distinctly non-Gaussian. We extend the Doroshkevich formula for the joined distribution of eigenvalues to two-dimensional fields and evaluate the two- and three-point correlation functions. In addition, we assess the number densities of singular points of the eigenvalue fields and find their corresponding two- and three-point correlation functions. The incentive for the present study is based on our interest in developing a fully analytical theory for the structure and dynamics of the cosmic web. The tidal forces and the resulting mass element deformation shape the prominent anisotropic wall-like and filamentary components of the cosmic web. Less well-known is that the web-like spatial pattern is already recognizable in the primordial tidal and deformation eigenvalue field. Against the full phase-space assessment of structure formation in the Universe, the caustic skeleton theory entails an analytical framework for the non-linear evolution of the cosmic web. It accomplishes this by describing the folding of the dark matter sheet and quantifying the emerging caustic singularities, which are fully specified by the spatial properties of the deformation eigenvalues and eigenvectors. Finally, the eigenvalues of the primordial tidal tensor are crucial in the generation of the angular momentum of galaxies. Understanding their spatial distribution is a critical element in predicting the resulting rotation amplitude and orientation.

The intrinsic alignment of red galaxies in DES Y1 redMaPPer galaxy clusters

ABSTRACT Clusters of galaxies trace the most non-linear peaks in the cosmic density field. The weak gravitational lensing of background galaxies by clusters can allow us to infer their masses. However, galaxies associated with the local environment of the cluster can also be intrinsically aligned due to the local tidal gradient, contaminating any cosmology derived from the lensing signal. We measure this intrinsic alignment in Dark Energy Survey (DES) Year 1 redMaPPer clusters. We find evidence of a non-zero mean radial alignment of galaxies within clusters between redshifts 0.1–0.7. We find a significant systematic in the measured ellipticities of cluster satellite galaxies that we attribute to the central galaxy flux and other intracluster light. We attempt to correct this signal, and fit a simple model for intrinsic alignment amplitude (AIA) to the measurement, finding AIA = 0.15 ± 0.04, when excluding data near the edge of the cluster. We find a significantly stronger alignment of the central galaxy with the cluster dark matter halo at low redshift and with higher richness and central galaxy absolute magnitude (proxies for cluster mass). This is an important demonstration of the ability of large photometric data sets like DES to provide direct constraints on the intrinsic alignment of galaxies within clusters. These measurements can inform improvements to small-scale modelling and simulation of the intrinsic alignment of galaxies to help improve the separation of the intrinsic alignment signal in weak lensing studies.

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.

Reconstruction of weak lensing mass maps for non-Gaussian studies in the celestial sphere

We present a novel method for reconstructing weak lensing mass or convergence maps as a probe to study non-Gaussianities in the cosmic density field. While previous surveys have relied on a flat-sky approximation, forthcoming Stage IV surveys will cover such large areas with a large field of view (FOV) to motivate mass reconstruction on the sphere. Here, we present an improved Kaiser-Squires (KS+) mass inversion method using a HEALPix pixelisation of the sphere while controlling systematic effects. As in the KS+ methodology, the convergence maps were reconstructed without noise regularisation to preserve the information content and allow for non-Gaussian studies. The results of this new method were compared with those of the Kaiser-Squires (KS) estimator implemented on the curved sky using high-resolution realistic N-body simulations. The quality of the method was evaluated by estimating the two-point correlation functions, third- and fourth-order moments, and peak counts of the reconstructed convergence maps. The effects of masking, sampling, and noise were tested. We also examined the systematic errors introduced by the flat-sky approximation. We show that the improved Kaiser-Squires on the sphere (SKS+) method systematically improves inferred correlation errors by ∼10 times and provides on average a 20–30 % better maximum signal-to-noise peak estimation compared to Kaiser-Squires on the sphere (SKS). We also show that the SKS+ method is nearly unbiased and reduces errors by a factor of about 2 and 4 in the third- and fourth-order moments, respectively. Finally, we show how the reconstruction of the convergence field directly on the celestial sphere eliminates the projection effects and allows the exclusion or consideration of a specific region of the sphere in the processing.

The time evolution of bias

ABSTRACT We investigate the time evolution of bias of cosmic density fields. We perform numerical simulations of the evolution of the cosmic web for the conventional Λ cold dark matter (ΛCDM) model. The simulations cover a wide range of box sizes $L=256\rm{-}1024\,h^{-1}\, {\rm Mpc}$, and epochs from very early moments z = 30 to the present moment z = 0. We calculate spatial correlation functions of galaxies, ξ(r), using dark matter particles of the biased Lambda cold dark mattter (ΛCDM) simulation. We analyse how these functions describe biasing properties of the evolving cosmic web. We find that for all cosmic epochs the bias parameter, defined through the ratio of correlation functions of selected samples and matter, depends on two factors: the fraction of matter in voids and in the clustered population, and the luminosity (mass) of galaxy samples. Gravity cannot evacuate voids completely, thus there is always some unclustered matter in voids, and the bias parameter of galaxies is always greater than unity, over the whole range of evolution epochs. We find that for all cosmic epochs bias parameter values form regular sequences, depending on galaxy luminosity (particle density limit), and decreasing with time.

Field-based physical inference from peculiar velocity tracers

ABSTRACT We present a proof-of-concept Bayesian hierarchical modelling approach to reconstruct the initial cosmic matter density field constrained by peculiar velocity observations. Using a model for the gravitational evolution of dark matter to connect the initial conditions to late-time observations, it reconstructs the late-time density and velocity fields as natural byproducts. We implement this field-based physical inference approach by adapting the Bayesian Origin Reconstruction from Galaxies ($\small {\rm BORG}$) algorithm, which explores the high-dimensional posterior through the use of Hamiltonian Monte Carlo sampling. We test the self-consistency of the method using random sets of tracers, and assess its accuracy in a more complex scenario where peculiar velocity tracers are mock haloes drawn from $\small {\rm GADGET2}$ N-body simulations. We find that our framework self-consistently infers the initial conditions, density and velocity fields, and shows some robustness to model mis-specification. Compared with the approach of constrained Gaussian random fields/Wiener filtering, the hierarchical model produces more accurate final density and velocity field reconstructions. It also allows us to constrain the initial conditions by peculiar velocity observations, complementing in this aspect other field-based approaches based on alternative cosmological observables such as galaxy clustering or weak lensing.

Covariances of density probability distribution functions. Lessons from hierarchical models

Context. Statistical properties of the cosmic density fields are to a large extent encoded in the shape of the one-point density probability distribution functions (PDF) as measured in surveys. In order to successfully exploit such observables, a detailed functional form of the covariance matrix of the one-point PDF is needed.Aims. The objectives are to model the properties of this covariance for general stochastic density fields and for stochastic fields that reproduce the properties expected in cosmology. The accuracy of the proposed forms is evaluated in specific cases.Methods. The study was conducted in a cosmological context and determined whether the density is defined absolutely or relatively to the sample mean density. Leading and subleading contributions were identified within a large class of models, the so-called hierarchical models. They come from either large or short separation contributions. The validity of the proposed forms for the covariance matrix was assessed with the help of a toy model, the minimum tree model, for which a corpus of exact results could be obtained (forms of the one- and two-point PDF, large-scale density-bias functions, and full covariance matrix of the one-point PDF).Results. It is first shown that the covariance matrix elements are directly related to the spatial average of the two-point density PDF within the sample. The dominant contribution to this average is explicitly given for hierarchical models (coming from large scale contribution), which leads to the construction of specific density-bias functions. However, this contribution alone cannot be used to construct an operational likelihood function. Subdominant large-scale effects are found to provide corrective terms, but also a priori lead to limited information on the covariance matrix. Short distance effects are found to be more important but more difficult to derive as they depend more on the details of the model. However, a simple and generic form of these contributions is proposed. Detailed comparisons in the context of the Rayleigh-Levy flight model show that the large-scale effects capture the bulk of the supersample effects and that, by adding the short-distance contributions, a qualitatively correct model of the likelihood function can be obtained.

Numerical investigation of non-Gaussianities in the phase and modulus of density Fourier modes

ABSTRACT We numerically investigate the non-Gaussianities in the late-time cosmological density field in Fourier space. We explore various statistics, including the two- and three-point probability distribution function (PDF) of phase and modulus, and their two- and three-point correlation function. Significant non-Gaussianity is observed for certain configurations. Comparing the measurement from simulation with the theoretical expansion prediction, we find that for (600 Mpc h-1)3 volume, the $\mathcal {O}(V^{-1/2})$ order term alone is sufficiently accurate to describe all the measured non-Gaussianities in not only the PDFs, but also the correlations. We also numerically find that the phase-modulus cross-correlation contributes $\sim 50{{\ \rm per\ cent}}$ to the bispectrum, further verifying the accuracy of the $\mathcal {O}(V^{-1/2})$ order prediction. This work demonstrates that the non-Gaussianity of cosmic density field is simpler in Fourier space, and may facilitate the data analysis in the era of precision cosmology.

Impact of thermal Sunyaev–Zeldovich effect on cross-correlations between Planck cosmic microwave background lensing and SDSS galaxy density fields

ABSTRACT Residual foreground contamination by thermal Sunyaev–Zeldovich (tSZ) effect from galaxy clusters in cosmic microwave background (CMB) maps propagates into the reconstructed CMB lensing field, and thus biases the intrinsic cross-correlation between CMB lensing and large-scale structure (LSS). Through stacking analysis, we show that residual tSZ contamination causes an increment of lensing convergence in the central part of the clusters and a decrement of lensing convergence in the cluster outskirts. We quantify the impact of residual tSZ contamination on cross-correlations between the Planck 2018 CMB lensing convergence maps and the Sloan Digital Sky Survey-IV galaxy density data through cross-power spectrum computation. In contrast with the Planck 2018 tSZ-deprojected smica lensing map, our analysis using the tSZ-contaminated smica lensing map measures an $\sim\!2.5{{\ \rm per\,cent}}$ negative bias at multipoles ℓ ≲ 500 and transits to an $\sim\!9{{\ \rm per\,cent}}$ positive bias at ℓ ≳ 1500, which validates earlier theoretical predictions of the overall shape of such tSZ-induced spurious cross-correlation. The tSZ-induced lensing convergence field in Planck CMB data is detected with more than 1σ significance at ℓ ≲ 500 and more than 14σ significance at ℓ ≳ 1500, yielding an overall 14.8σ detection. We also show that masking galaxy clusters in CMB data is not sufficient to eliminate the spurious lensing signal, still detecting a non-negligible bias with 5.5σ significance on cross-correlations with galaxy density fields. Our results emphasize how essential it is to deproject the tSZ effect from CMB maps at the component separation stage and adopt tSZ-free CMB lensing maps for cross-correlations with LSS data.

Density reconstruction from biased tracers and its application to primordial non-Gaussianity

Large-scale Fourier modes of the cosmic density field are of great value for learning about cosmology because of their well-understood relationship to fluctuations in the early universe. However, cosmic variance generally limits the statistical precision that can be achieved when constraining model parameters using these modes as measured in galaxy surveys, and moreover, these modes are sometimes inaccessible due to observational systematics or foregrounds. For some applications, both limitations can be circumvented by reconstructing large-scale modes using the correlations they induce between smaller-scale modes of an observed tracer (such as galaxy positions). In this paper, we further develop a formalism for this reconstruction, using a quadratic estimator similar to the one used for lensing of the cosmic microwave background. We incorporate nonlinearities from gravity, nonlinear biasing, and local-type primordial non-Gaussianity, and verify that the estimator gives the expected results when applied to N-body simulations. We then carry out forecasts for several upcoming surveys, demonstrating that, when reconstructed modes are included alongside directly-observed tracer density modes, constraints on local primordial non-Gaussianity are generically tightened by tens of percents compared to standard single-tracer analyses. In certain cases, these improvements arise from cosmic variance cancellation, with reconstructed modes taking the place of modes of a separate tracer, thus enabling an effective "multitracer" approach with single-tracer observations.

C3: Cluster Clustering Cosmology. ii. First Detection of the Baryon Acoustic Oscillations Peak in the Three-point Correlation Function of Galaxy Clusters

Abstract Third-order statistics of the cosmic density field provides a powerful cosmological probe containing synergistic information to the more commonly explored second-order statistics. Here, we exploit a spectroscopic catalog of 72,563 clusters of galaxies extracted from the Sloan Digital Sky Survey (SDSS), providing the first detection of the baryon acoustic oscillations (BAO) peak in the three-point correlation function (3PCF) of galaxy clusters. We measure and analyze both the connected and the reduced 3PCF of SDSS clusters from intermediate (r ∼ 10 Mpc h−1) up to large (r ∼ 140 Mpc h−1) scales, exploring a variety of different configurations. From the analysis of reduced 3PCF at intermediate scales, in combination with the analysis of the two-point correlation function, we constrain both the cluster linear and nonlinear bias parameters, b 1 = 2.75 ± 0.03 and b 2 = 1.2 ± 0.5. We analyze the measurements of the 3PCF at larger scales, comparing them with theoretical models. The data show clear evidence of the BAO peak in different configurations, which appears more visible in the reduced 3PCF rather than in the connected one. From the comparison between theoretical models that do or do not consider the BAO peak, we obtain a quantitative estimate of this evidence, with a Δχ 2 between 2 and 94, depending on the considered configuration. Finally, we set up a generic framework to estimate the expected signal-to-noise ratio of the BAO peak in the 3PCF, exploring different possible definitions that can be used to forecast the most favorable configurations to be explored in future surveys, and applying it to the case of the Euclid mission.

Medusa: Minkowski functionals estimated from Delaunay tessellations of the three-dimensional large-scale structure

ABSTRACT Minkowski functionals (MFs) are a set of statistics that characterize the geometry and topology of the cosmic density field and contain complementary information to the standard two-point analyses. We present medusa, an implementation of an accurate method for estimating the MFs of three-dimensional point distributions. These estimates are inferred from triangulated isodensity surfaces that are constructed from the Delaunay tessellation of the input point sample. medusa can account for periodic boundary conditions, which is crucial for the analysis of N-body simulations. We validate our code against several test samples with known MFs, including Gaussian random fields with a ΛCDM power spectrum, and find excellent agreement with the theory predictions. We use medusa to measure the MFs of synthetic galaxy catalogues constructed from N-body simulations. Our results show clearly non-Gaussian signatures that arise from the non-linear gravitational evolution of the density field. We find that, although redshift-space distortions change our MFs estimates, their impact is considerably reduced if these measurements are expressed as a function of the volume-filling fraction. We also show that the effect of Alcock–Paczynski (AP) distortions on the MFs can be described by scaling them with different powers of the isotropic AP parameter q defined in terms of the volume-averaged distance DV(z). Thus the MFs estimates by medusa are useful probes of non-linearities in the density field, and the expansion and growth of structure histories of the Universe.

Evolution of skewness and kurtosis of cosmic density fields

Aims. We investigate the evolution of the one-point probability distribution function (PDF) of the dark matter density field and the evolution of its moments for fluctuations that are Gaussian in the linear regime. Methods. We performed numerical simulations of the evolution of the cosmic web for the conventional ΛCDM model. The simulations covered a wide range of box sizes L = 256 − 4000 h−1 Mpc, mass, and force resolutions, and epochs from very early moments z = 30 to the present moment z = 0. We calculated density fields with various smoothing lengths to determine the dependence of the density field on the smoothing scale. We calculated the PDF and its moments variance, skewness, and kurtosis. We determined the dependence of these parameters on the evolutionary epoch z, on the smoothing length Rt, and on the rms deviation of the density field σ using a cubic-cell and top-hat smoothing with kernels 0.4 h−1 Mpc ≤ Rt ≤ 32 h−1 Mpc. Results. We focus on the third (skewness S) and fourth (kurtosis K) moments of the distribution functions: their dependence on the smoothing scale Rt, the amplitude of the fluctuations σ, and the redshift z. Moments S and K, calculated for density fields at different cosmic epochs and smoothed with various scales, characterise the evolution of different structures of the web. Moments calculated with small-scale smoothing (Rt ≈ (1 − 4) h−1 Mpc) characterise the evolution of the web on cluster-type scales. Moments found with strong smoothing (Rt ≳ (5 − 15) h−1 Mpc) describe the evolution of the web on supercluster scales. During the evolution, the reduced skewness S3 = S/σ and reduced kurtosis S4 = K/σ2 present a complex behaviour: at a fixed redshift, curves of S3(σ) and S4(σ) steeply increase with σ at σ ≲ 1 and then flatten out and become constant at σ ≳ 2. When we fixed the smoothing scale Rt, the curves at large σ started to gradually decline after reaching the maximum at σ ≈ 2. We provide accurate fits for the evolution of S3, 4(σ, z). Skewness and kurtosis approach constant levels at early epochs S3(σ)≈3 and S4(σ)≈15. Conclusions. Most of the statistics of dark matter clustering (e.g. halo mass function or concentration-mass relation) are nearly universal: they mostly depend on the σ with a relatively modest correction to apparent dependence on the redshift. We find just the opposite for skewness and kurtosis: the dependence of the moments on the evolutionary epoch z and smoothing length Rt is very different. Together, they uniquely determine the evolution of S3, 4(σ). The evolution of S3 and S4 cannot be described by current theoretical approximations. The often used lognormal distribution function for the PDF fails to even qualitatively explain the shape and evolution of S3 and S4.

Expansion series of the pairwise velocity generating function and its implications on redshift space distortion modeling

The pairwise velocity generating function G has a deep connection with both the pairwise velocity probability distribution function and modeling of redshift space distortion (RSD). Its implementation into RSD modeling is often faciliated by expansion into a series of pairwise velocity moments . Motivated by the logrithmic transformation of the cosmic density field, we investigate an alternative expansion into series of pairwise velocity cumulants . We numerically evaluate the convergence rate of the two expansions, with three 30723 particle simulations of the CosmicGrowth N-body simulation series. (1) We find that the cumulant expansion performs significantly better, for all the halo samples and redshifts investigated. (2) For modeling RSD at k ∥ < 0.1h Mpc−1, including only the n = 1,2 cumulants is sufficient. (3) But for modeling RSD at k ∥ = 0.2h Mpc−1, we need and only need the n = 1,2,3,4 cumulants. These results provide specific requirements on RSD modeling in terms of m-th order statistics of the large-scale structure.

Three-dimensional Reconstruction of Weak-lensing Mass Maps with a Sparsity Prior. I. Cluster Detection

Abstract We propose a novel method to reconstruct high-resolution three-dimensional mass maps using data from photometric weak-lensing surveys. We apply an adaptive LASSO algorithm to perform a sparsity-based reconstruction on the assumption that the underlying cosmic density field is represented by a sum of Navarro–Frenk–White halos. We generate realistic mock galaxy shear catalogs by considering the shear distortions from isolated halos for the configurations matched to the Subaru Hyper Suprime-Cam Survey with its photometric redshift estimates. We show that the adaptive method significantly reduces line-of-sight smearing that is caused by the correlation between the lensing kernels at different redshifts. Lensing clusters with lower mass limits of 1014.0 h−1 M ⊙, 1014.7 h−1 M ⊙, 1015.0 h−1 M ⊙ can be detected with 1.5σ confidence at the low (z &lt; 0.3), median (0.3 ≤ z &lt; 0.6), and high (0.6 ≤ z &lt; 0.85) redshifts, respectively, with an average false detection rate of 0.022 deg−2. The estimated redshifts of the detected clusters are systematically lower than the true values by Δz ∼ 0.03 for halos at z ≤ 0.4, but the relative redshift bias is below 0.5% for clusters at 0.4 &lt; z ≤ 0.85. The standard deviation of the redshift estimation is 0.092. Our method enables direct three-dimensional cluster detection with accurate redshift estimates.

Ray-tracing log-normal simulation for weak gravitational lensing: applicationto the cross-correlation with galaxies

We present an algorithm to self-consistently generate mock weak gravitational lensing convergence fields and galaxy distributions in redshift space. We generate three-dimensional cosmic density fields that follow a log-normal distribution, and ray-trace them to produce convergence maps. As we generate the galaxy distribution from the same density fields in a manner consistent with ray-tracing, the galaxy-convergence cross-power spectrum measured from the mock agrees with the theoretical expectation with high precision.We use this simulation to forecast the quality of galaxy-shear cross-correlation measurements from the SubaruHyper Suprime-Cam (HSC) and Prime Focus Spectrograph (PFS) surveys.We find that the nominal HSC and PFS surveys would detect the cross power spectra with signal-to-noise ratios of 20 and 5 at the lowest (z = 0.7) and highest (z = 2.2) redshift bins, respectively.

Bayesian forward modelling of cosmic shear data

ABSTRACT We present a Bayesian hierarchical modelling approach to infer the cosmic matter density field, and the lensing and the matter power spectra, from cosmic shear data. This method uses a physical model of cosmic structure formation to infer physically plausible cosmic structures, which accounts for the non-Gaussian features of the gravitationally evolved matter distribution and light-cone effects. We test and validate our framework with realistic simulated shear data, demonstrating that the method recovers the unbiased matter distribution and the correct lensing and matter power spectrum. While the cosmology is fixed in this test, and the method employs a prior power spectrum, we demonstrate that the lensing results are sensitive to the true power spectrum when this differs from the prior. In this case, the density field samples are generated with a power spectrum that deviates from the prior, and the method recovers the true lensing power spectrum. The method also recovers the matter power spectrum across the sky, but as currently implemented, it cannot determine the radial power since isotropy is not imposed. In summary, our method provides physically plausible inference of the dark matter distribution from cosmic shear data, allowing us to extract information beyond the two-point statistics and exploiting the full information content of the cosmological fields.

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.