Weak Lensing Convergence Research Articles

Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

ABSTRACT We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum–bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelized prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the six-point correlation function and supersample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10 per cent on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimize future analyses of the weak lensing bispectrum. We find that, ignoring systematics, five equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

The self-similarity of weak lensing peaks

ABSTRACT We study the statistics of weak lensing convergence peaks, such as their abundance and two-point correlation function (2PCF), for a wide range of cosmological parameters Ωm and σ8 within the standard ΛCDM paradigm, focusing on intermediate-height peaks with signal-to-noise ratio (SNR) of 1.5–3.5. We find that the cosmology dependence of the peak abundance can be described by a one-parameter fitting formula that is accurate to within $\sim 3{{\ \rm per\ cent}}$. The peak 2PCFs are shown to feature a self-similar behaviour: if the peak separation is rescaled by the mean interpeak distance, catalogues with different minimum peak SNR values have identical clustering, which suggests that the peak abundance and clustering are closely interconnected. A simple fitting model for the rescaled 2PCF is given, which together with the peak abundance model above can predict peak 2PCFs with an accuracy better than $\sim 5{{\ \rm per\ cent}}$. The abundance and 2PCFs for intermediate peaks have very different dependencies on Ωm and σ8, implying that their combination can be used to break the degeneracy between these two parameters.

Dark Energy Survey year 1 results: Joint analysis of galaxy clustering, galaxy lensing, and CMB lensing two-point functions

We perform a joint analysis of the auto and cross-correlations between three cosmic fields: the galaxy density field, the galaxy weak lensing shear field, and the cosmic microwave background (CMB) weak lensing convergence field. These three fields are measured using roughly 1300 sq. deg. of overlapping optical imaging data from first year observations of the Dark Energy Survey and millimeter-wave observations of the CMB from both the South Pole Telescope Sunyaev-Zel'dovich survey and Planck. We present cosmological constraints from the joint analysis of the two-point correlation functions between galaxy density and galaxy shear with CMB lensing. We test for consistency between these measurements and the DES-only two-point function measurements, finding no evidence for inconsistency in the context of flat $\Lambda$CDM cosmological models. Performing a joint analysis of five of the possible correlation functions between these fields (excluding only the CMB lensing autospectrum) yields $S_{8}\equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3} = 0.782^{+0.019}_{-0.025}$ and $\Omega_{\rm m}=0.260^{+0.029}_{-0.019}$. We test for consistency between these five correlation function measurements and the Planck-only measurement of the CMB lensing autospectrum, again finding no evidence for inconsistency in the context of flat $\Lambda$CDM models. Combining constraints from all six two-point functions yields $S_{8}=0.776^{+0.014}_{-0.021}$ and $\Omega_{\rm m}= 0.271^{+0.022}_{-0.016}$. These results provide a powerful test and confirmation of the results from the first year DES joint-probes analysis.

Forecasts of cosmological constraints from Type Ia supernovae including the weak-lensing convergence

We investigate how the cosmological constraints from SNe Ia are improved by including the effects of weak-lensing convergence. To do so, we introduce the lognormal function as the convergence PDF modeling the lensing scatter of SN Ia magnitude, and apply a sample selection for SNe Ia to avoid strongly lensed samples. Comparing with the contribution of other uncertainties (e.g., the intrinsic magnitude scatter), we find that the lensing effect is dominant at z > 1. Then forecasting the parameter constraints for the Wide-Field InfraRed Survey Telescope survey, we show that considering the weak-lensing effect, the constraints on the density parameters Ωm or ΩΛ, and the dark energy equation of state w are improved, especially for SNe Ia samples at higher redshift z > 1. Furthermore, we see that the degeneracy between the total mass of neutrino Σ mν and the (cold) dark matter density parameter Ωc can be resolved.

Constraining neutrino mass with weak lensing Minkowski Functionals

The presence of massive neutrinos affects structure formation, leaving imprints on large-scale structure observables such as the weak lensing field. The common lensing analyses with two-point statistics are insensitive to the large amount of non-Gaussian information in the density field. We investigate non-Gaussian tools, in particular the Minkowski Functionals (MFs)—morphological descriptors including area, perimeter, and genus—in an attempt to recover the higher-order information. We use convergence maps from the Cosmological Massive Neutrino Simulations (MassiveNus) and assume galaxy noise, density, and redshift distribution for an LSST-like survey. We show that MFs are sensitive to the neutrino mass sum through non-Gaussian features of the lensing field, with a redshift dependence different from that of the power spectrum. We find that redshift tomography significantly improves the constraints on neutrino mass for MFs, compared to the improvements for the convergence power spectrum. We attribute this to the stronger redshift dependence of neutrino effects on small scales. We then build an emulator to model the power spectrum and MFs, and study the constraints on [Mν, Ωm, As] from the power spectrum, MFs, and their combination. We show that, for weak lensing convergence, MFs significantly outperform the power spectrum in constraining neutrino mass, by more than a factor of four. However, a thorough study of the impact from systematics such as baryon physics, galaxy shape and redshift biases will be important to realize the full potential of MFs.

Painting with baryons: augmenting N-body simulations with gas using deep generative models

Abstract Running hydrodynamical simulations to produce mock data of large-scale structure and baryonic probes, such as the thermal Sunyaev–Zeldovich (tSZ) effect, at cosmological scales is computationally challenging. We propose to leverage the expressive power of deep generative models to find an effective description of the large-scale gas distribution and temperature. We train two deep generative models, a variational auto-encoder and a generative adversarial network, on pairs of matter density and pressure slices from the BAHAMAS hydrodynamical simulation. The trained models are able to successfully map matter density to the corresponding gas pressure. We then apply the trained models on 100 lines of sight from SLICS, a suite of N-body simulations optimized for weak lensing covariance estimation, to generate maps of the tSZ effect. The generated tSZ maps are found to be statistically consistent with those from BAHAMAS. We conclude by considering a specific observable, the angular cross-power spectrum between the weak lensing convergence and the tSZ effect and its variance, where we find excellent agreement between the predictions from BAHAMAS and SLICS, thus enabling the use of SLICS for tSZ covariance estimation.

Accurate analytic model for the thermal Sunyaev-Zel’dovich one-point probability distribution function

Non-Gaussian statistics of late-time cosmological fields contain information beyond that captured in the power spectrum. Here we focus on one such example: the one-point probability distribution function (PDF) of the thermal Sunyaev-Zel'dovich (tSZ) signal in maps of the cosmic microwave background (CMB). It has been argued that the one-point PDF is a near-optimal statistic for cosmological constraints from the tSZ signal, as most of the constraining power in tSZ $N$-point functions is contained in their amplitudes (rather than their shapes), which probe differently-weighted integrals over the halo mass function. In this paper, we develop a new analytic halo model for the tSZ PDF, discarding simplifying assumptions made in earlier versions of this approach. In particular, we account for effects due to overlaps of the tSZ profiles of different halos, as well as effects due to the clustering of halos. We verify the accuracy of our analytic model via comparison to numerical simulations. We demonstrate that this more accurate model is necessary for the analysis of the tSZ PDF in upcoming CMB experiments. The novel formalism developed here may be useful in modeling the one-point PDF of other cosmological observables, such as the weak lensing convergence field.

CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks

Inferring model parameters from experimental data is a grand challenge in many sciences, including cosmology. This often relies critically on high fidelity numerical simulations, which are prohibitively computationally expensive. The application of deep learning techniques to generative modeling is renewing interest in using high dimensional density estimators as computationally inexpensive emulators of fully-fledged simulations. These generative models have the potential to make a dramatic shift in the field of scientific simulations, but for that shift to happen we need to study the performance of such generators in the precision regime needed for science applications. To this end, in this work we apply Generative Adversarial Networks to the problem of generating weak lensing convergence maps. We show that our generator network produces maps that are described by, with high statistical confidence, the same summary statistics as the fully simulated maps.

Accurately computing weak lensing convergence

ABSTRACT Weak lensing will play an important role in future cosmological surveys, including e.g. Euclid and SKA. Sufficiently accurate theoretical predictions are important for correctly interpreting these surveys and hence for extracting correct cosmological parameter estimations. We quantify for the first time in a relativistic setting how many post-Born and lens–lens coupling corrections are required for sub-per cent accuracy of the theoretical weak lensing convergence for $z$ ≤ 2 (the primary weak lensing range for Euclid and SKA). We do this by ray tracing through a fully relativistic exact solution of the Einstein field equations, which consists of randomly packed mass-compensated underdensities of realistic amplitudes. We find that including lens–lens coupling terms and post-Born corrections up to second and third order respectively is sufficient for sub-per cent accuracy of the convergence along $94{{\ \rm per\ cent}}$ of the studied light rays. We also find that a significant percentage of the studied rays have post-Born corrections of size over $10{{\ \rm per\ cent}}$ of the usual gravitational convergence, κ(1), and several rays even have post-Born corrections several times the size of κ(1) at $z$ = 2.

Cosmic convergence and shear with extended sources

The standard theory of weak gravitational lensing relies on the approximation that light beams are infinitesimal. Our recent work showed that the finite size of sources, and the associated light beams, can cause nonperturbative corrections to the weak-lensing convergence and shear. This article thoroughly investigates these corrections in a realistic cosmological model. The continuous transition from infinitesimal to finite beams is understood, and reveals that the previous results overestimated finite-beam effects due to simplistic assumptions on the distribution of matter in the Universe. In a KiloDegree Survey-like setting, finite-beam corrections to the cosmic shear remain subpercent, while percent-level corrections are only reached on subarcmin scales. This article thus demonstrates the validity of the infinitesimal-beam approximation in the interpretation of current weak-lensing data.

An improved cosmological parameter inference scheme motivated by deep learning

Dark matter cannot be observed directly, but its weak gravitational lensing slightly distorts the apparent shapes of background galaxies, making weak lensing one of the most promising probes of cosmology. Several observational studies have measured the effect, and there are currently running1,2 and planned efforts3,4 to provide even larger and higher-resolution weak lensing maps. Owing to nonlinearities on small scales, the traditional analysis with two-point statistics does not fully capture all of the underlying information5. Multiple inference methods have been proposed to extract more details based on higher-order statistics6,7, peak statistics8–13, Minkowski functionals14–16 and recently convolutional neural networks17,18. Here we present an improved convolutional neural network that gives significantly better estimates of the Ωm and σ8 cosmological parameters from simulated weak lensing convergence maps than state-of-art methods and that is also free of systematic bias. We show that the network exploits information in the gradients around peaks, and with this insight we have constructed an easy-to-understand and robust peak-counting algorithm based on the steepness of peaks, instead of their heights. The proposed scheme is even more accurate than the neural network on high-resolution noiseless maps. With shape noise and lower resolution, its relative advantage deteriorates, but it remains more accurate than peak counting. A convolutional neural network estimates cosmological parameters from simulated weak lensing convergence maps in an unbiased way. The network analysis motivates a new and robust convergence peak-counting algorithm based on the steepness of peak heights.

Weak lensing by voids in weak lensing maps

ABSTRACT Cosmic voids are an important probe of large-scale structure that can constrain cosmological parameters and test cosmological models. We present a new paradigm for void studies: void detection in weak lensing convergence maps. This approach identifies objects that relate directly to our theoretical understanding of voids as underdensities in the total matter field and presents several advantages compared to the customary method of finding voids in the galaxy distribution. We exemplify this approach by identifying voids using the weak lensing peaks as tracers of the large-scale structure. We find self-similarity in the void abundance across a range of peak signal-to-noise selection thresholds. The voids obtained via this approach give a tangential shear signal up to ∼40 times larger than voids identified in the galaxy distribution.

On the effect of projections on convergence peak counts and Minkowski functionals

The act of projecting data sampled on the surface of the celestial sphere onto a regular grid on the plane can introduce error and a loss of information. This paper evaluates the effects of different planar projections on non-Gaussian statistics of weak lensing convergence maps. In particular we investigate the effect of projection on peak counts and Minkowski Functionals (MFs) derived from convergence maps and the suitability of a number of projections at matching the peak counts and MFs obtained from a sphere. We find that the peak counts derived from planar projections consistently overestimate the counts at low SNR thresholds and underestimate at high SNR thresholds across the projections evaluated, although the difference is reduced when smoothing of the maps is increased. In the case of the Minkowski Functionals, V0 is minimally affected by projection used, while projected V1 and V2 are consistently overestimated with respect to the spherical case.

Weak lensing probe of cubic Galileon model

The cubic Galileon model containing the lowest non-trivial order action of the full Galileon action can produce the stable late-time cosmic acceleration. This model can have a significant role in the growth of structures. The signatures of the cubic Galileon model in the structure formation can be probed by the weak lensing statistics. Weak lensing convergence statistics is one of the strongest probes to the structure formation and hence it can probe the dark energy or modified theories of gravity models. In this work, we investigate the detectability of the cubic Galileon model from the ΛCDM model or from the canonical quintessence model through the convergence power spectrum and bi-spectrum.

Complete super-sample lensing covariance in the response approach

We derive the complete super-sample covariance (SSC) of the matter and weak lensing convergence power spectra using the power spectrum response formalism to accurately describe the coupling of super- to sub-survey modes. The SSC term is completely characterized by the survey window function, the nonlinear matter power spectrum and the full first-order nonlinear power spectrum response function, which describes the response to super-survey density and tidal field perturbations. Generalized separate universe simulations can efficiently measure these responses in the nonlinear regime of structure formation, which is necessary for lensing applications. We derive the lensing SSC formulae for two cases: one under the Limber and flat-sky approximations, and a more general one that goes beyond the Limber approximation in the super-survey mode and is valid for curved sky applications. Quantitatively, we find that for sky fractions fsky ≈ 0.3 and a single source redshift at zS=1, the use of the flat-sky and Limber approximation underestimates the total SSC contribution by ≈ 10%. The contribution from super-survey tidal fields to the lensing SSC, which has not been included in cosmological analyses so far, is shown to represent about 5% of the total lensing covariance on multipoles ℓ1,ℓ2 ≳ 300. The SSC is the dominant off-diagonal contribution to the total lensing covariance, making it appropriate to include these tidal terms and beyond flat-sky/Limber corrections in cosmic shear analyses.

General relativistic corrections to the weak lensing convergence power spectrum

We compute the weak lensing convergence power spectrum, $C^{\kappa\kappa}(\theta)$, in a dust-filled universe using fully non-linear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, $\ell ~ 2-3$, and percent-level corrections at intermediate angular scales of $\ell ~ 20-30$.

KiDS-450: cosmological constraints from weak lensing peak statistics – I. Inference from analytical prediction of high signal-to-noise ratio convergence peaks

This paper is the first of a series of papers constraining cosmological parameters with weak lensing peak statistics using $\sim 450~\rm deg^2$ of imaging data from the Kilo Degree Survey (KiDS-450). We measure high signal-to-noise ratio (SNR: $\nu$) weak lensing convergence peaks in the range of $3<\nu<5$, and employ theoretical models to derive expected values. These models are validated using a suite of simulations. We take into account two major systematic effects, the boost factor and the effect of baryons on the mass-concentration relation of dark matter haloes. In addition, we investigate the impacts of other potential astrophysical systematics including the projection effects of large scale structures, intrinsic galaxy alignments, as well as residual measurement uncertainties in the shear and redshift calibration. Assuming a flat $\Lambda$CDM model, we find constraints for $S_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm m}/0.3)^{0.5}=0.746^{+0.046}_{-0.107}$ according to the degeneracy direction of the cosmic shear analysis and $\Sigma_{\rm 8}=\sigma_{\rm 8}(\Omega_{\rm m}/0.3)^{0.38}=0.696^{+0.048}_{-0.050}$ based on the derived degeneracy direction of our high-SNR peak statistics. The difference between the power index of $S_{\rm 8}$ and in $\Sigma_{\rm 8}$ indicates that combining the two probes has the potential to break the degeneracy in $\sigma_{\rm 8}$ and $\Omega_{\rm m}$. Our results are consistent with the cosmic shear tomographic correlation analysis of the same dataset and $\sim 2\sigma$ lower than the Planck 2016 results.

Constraints on the dark matter and dark energy interactions from weak lensing bispectrum tomography

We estimate uncertainties of cosmological parameters for phenomenological interacting dark energy models using weak lensing convergence power spectrum and bispectrum. We focus on the bispectrum tomography and examine how well the weak lensing bispectrum with tomography can constrain the interactions between dark sectors, as well as other cosmological parameters. Employing the Fisher matrix analysis, we forecast parameter uncertainties derived from weak lensing bispectra with a two-bin tomography and place upper bounds on strength of the interactions between the dark sectors. The cosmic shear will be measured from upcoming weak lensing surveys with high sensitivity, thus it enables us to use the higher order correlation functions of weak lensing to constrain the interaction between dark sectors and will potentially provide more stringent results with other observations combined.

Consistency relations for large-scale structures: Applications for the integrated Sachs-Wolfe effect and the kinematic Sunyaev-Zeldovich effect

Consistency relations of large-scale structures provide exact nonperturbative results for cross-correlations of cosmic fields in the squeezed limit. They only depend on the equivalence principle and the assumption of Gaussian initial conditions, and remain nonzero at equal times for cross-correlations of density fields with velocity or momentum fields, or with the time derivative of density fields. We show how to apply these relations to observational probes that involve the integrated Sachs-Wolfe effect or the kinematic Sunyaev-Zeldovich effect. In the squeezed limit, this allows us to express the three-point cross-correlations, or bispectra, of two galaxy or matter density fields, or weak lensing convergence fields, with the secondary cosmic microwave background distortion in terms of products of a linear and a nonlinear power spectrum. In particular, we find that cross-correlations with the integrated Sachs-Wolfe effect show a specific angular dependence. These results could be used to test the equivalence principle and the primordial Gaussianity, or to check the modeling of large-scale structures.

Probing dark energy using convergence power spectrum and bi-spectrum

Weak lensing convergence statistics is a powerful tool to probe dark energy. Dark energy plays an important role to the structure formation and the effects can be detected through the convergence power spectrum, bi-spectrum etc. One of the most promising and simplest dark energy model is the ΛCDM . However, it is worth investigating different dark energy models with evolving equation of state of the dark energy. In this work, detectability of different dark energy models from ΛCDM model has been explored through convergence power spectrum and bi-spectrum.