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Subhalo abundance matching (SHAM) is widely used for connecting galaxies to dark matter haloes. In SHAM, galaxies and (sub-)haloes are sorted according to their mass (or mass proxy) and matched by their rank order. In this work, we show that SHAM is the solution of the optimal transport (OT) problem on empirical distributions (samples or catalogues) for any metric transport cost function. In the limit of large number of samples, it converges to the solution of the OT problem between continuous distributions. We propose SHAM-OT: a formulation of abundance matching where the halo-galaxy relation is obtained as the optimal transport plan between galaxy and halo mass functions. By working directly on these (discretized) functions, SHAM-OT eliminates the need for sampling or sorting and is solved using efficient OT algorithms at negligible compute and memory cost. Scatter in the galaxy-halo relation can be naturally incorporated through regularization of the transport plan. SHAM-OT can easily be generalized to multiple marginal distributions. We validate our method using analytical tests with varying cosmology and luminosity function parameters, and on simulated halo catalogues. The efficiency of SHAM-OT makes it particularly advantageous for Bayesian inference that requires marginalization over stellar mass or luminosity function uncertainties., Comment: 7 pages, 6 figures, submitted

Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using fixed summary statistics, are showing potential to break key degeneracies by better probe combination and will likely improve rapidly in the coming years as progress is made in the physical modelling through both software and hardware improvement. One key issue remains: unlike classical analysis, a convolutional neural network's decision process is hidden from the user as the network optimises millions of parameters with no direct physical meaning. This prevents a clear understanding of the potential limitations and biases of the analysis, making it hard to rely on as a main analysis method. In this work, we explore the behaviour of such a convolutional neural network through a novel method. Instead of trying to analyse a network a posteriori, i.e. after training has been completed, we study the impact on the constraining power of training the network and predicting parameters with degraded data where we removed part of the information. This allows us to gain an understanding of which parts and features of a large-scale structure survey are most important in the network's prediction process. We find that the network's prediction process relies on a mix of both Gaussian and non-Gaussian information, and seems to put an emphasis on structures whose scales are at the limit between linear and non-linear regimes., Comment: 11 pages, 13 figures, submitted to A&A

Large-scale structure surveys measure the shape and position of millions of galaxies in order to constrain the cosmological model with high precision. The resulting large data volume poses a challenge for the analysis of the data, from the estimation of photometric redshifts to the calibration of shape measurements. We present GalSBI, a model for the galaxy population, to address these challenges. This phenomenological model is constrained by observational data using simulation-based inference (SBI). The $\texttt{galsbi}$ Python package provides an easy interface to generate catalogs of galaxies based on the GalSBI model, including their photometric properties, and to simulate realistic images of these galaxies using the $\texttt{UFig}$ package., Comment: 10 pages, 5 figures, submitted to JOSS

With the rise of simulation-based inference (SBI) methods, simulations need to be fast as well as realistic. $\texttt{UFig v1}$ is a public Python package that generates simulated astronomical images with exceptional speed - taking approximately the same time as source extraction. This makes it particularly well-suited for simulation-based inference (SBI) methods where computational efficiency is crucial. To render an image, $\texttt{UFig}$ requires a galaxy catalog and a description of the point spread function (PSF). It can also add background noise, sample stars using the Besan\c{c}on model of the Milky Way, and run $\texttt{SExtractor}$ to extract sources from the rendered image. The extracted sources can be matched to the intrinsic catalog, flagged based on $\texttt{SExtractor}$ output and survey masks, and emulators can be used to bypass the image simulation and extraction steps. A first version of $\texttt{UFig}$ was presented in Berg\'e et al. (2013) and the software has since been used and further developed in a variety of forward modelling applications., Comment: 8 pages, 4 figures, submitted to JOSS

We present GalSBI, a phenomenological model of the galaxy population for cosmological applications using simulation-based inference. The model is based on analytical parametrizations of galaxy luminosity functions, morphologies and spectral energy distributions. Model constraints are derived through iterative Approximate Bayesian Computation, by comparing Hyper Suprime-Cam deep field images with simulations which include a forward model of instrumental, observational and source extraction effects. We developed an emulator trained on image simulations using a normalizing flow. We use it to accelerate the inference by predicting detection probabilities, including blending effects and photometric properties of each object, while accounting for background and PSF variations. This enables robustness tests for all elements of the forward model and the inference. The model demonstrates excellent performance when comparing photometric properties from simulations with observed imaging data for key parameters such as magnitudes, colors and sizes. The redshift distribution of simulated galaxies agrees well with high-precision photometric redshifts in the COSMOS field within $1.5\sigma$ for all magnitude cuts. Additionally, we demonstrate how GalSBI's redshifts can be utilized for splitting galaxy catalogs into tomographic bins, highlighting its potential for current and upcoming surveys. GalSBI is fully open-source, with the accompanying Python package, $\texttt{galsbi}$, offering an easy interface to quickly generate realistic, survey-independent galaxy catalogs., Comment: 43 pages, 14 figures, submitted

Laue tomography experiments retrieve the positions and orientations of crystal grains in a polycrystalline samples from diffraction patterns recorded at multiple viewing angles. The use of a broad wavelength spectrum beam can greatly reduce the experimental time, but poses a difficult challenge for the indexing of diffraction peaks in polycrystalline samples; the information about the wavelength of these Bragg peaks is absent and the diffraction patterns from multiple grains are superimposed. To date, no algorithms exist capable of indexing samples with more than about 500 grains efficiently. To address this need we present a novel method: Laue indexing with Optimal Transport (LaueOT). We create a probabilistic description of the multi-grain indexing problem and propose a solution based on Sinkhorn Expectation-Maximization method, which allows to efficiently find the maximum of the likelihood thanks to the assignments being calculated using Optimal Transport. This is a non-convex optimization problem, where the orientations and positions of grains are optimized simultaneously with grain-to-spot assignments, while robustly handling the outliers. The selection of initial prototype grains to consider in the optimization problem are also calculated within the Optimal Transport framework. LaueOT can rapidly and effectively index up to 1000 grains on a single large memory GPU within less than 30 minutes. We demonstrate the performance of LaueOT on simulations with variable numbers of grains, spot position measurement noise levels, and outlier fractions. The algorithm recovers the correct number of grains even for high noise levels and up to 70% outliers in our experiments. We compare the results of indexing with LaueOT to existing algorithms both on synthetic and real neutron diffraction data from well-characterized samples., Comment: Data and code available at https://github.com/LaueOT/laueotx. 19 Pages, 8 figures

Accurate redshift calibration is required to obtain unbiased cosmological information from large-scale galaxy surveys. In a forward modelling approach, the redshift distribution n(z) of a galaxy sample is measured using a parametric galaxy population model constrained by observations. We use a model that captures the redshift evolution of the galaxy luminosity functions, colours, and morphology, for red and blue samples. We constrain this model via simulation-based inference, using factorized Approximate Bayesian Computation (ABC) at the image level. We apply this framework to HSC deep field images, complemented with photometric redshifts from COSMOS2020. The simulated telescope images include realistic observational and instrumental effects. By applying the same processing and selection to real data and simulations, we obtain a sample of n(z) distributions from the ABC posterior. The photometric properties of the simulated galaxies are in good agreement with those from the real data, including magnitude, colour and redshift joint distributions. We compare the posterior n(z) from our simulations to the COSMOS2020 redshift distributions obtained via template fitting photometric data spanning the wavelength range from UV to IR. We mitigate sample variance in COSMOS by applying a reweighting technique. We thus obtain a good agreement between the simulated and observed redshift distributions, with a difference in the mean at the 1$\sigma$ level up to a magnitude of 24 in the i band. We discuss how our forward model can be applied to current and future surveys and be further extended. The ABC posterior and further material will be made publicly available at https://cosmology.ethz.ch/research/software-lab/ufig.html., Comment: Accepted for publication in JCAP. 35 pages, 9 figures

A forward modelling approach provides simple, fast and realistic simulations of galaxy surveys, without a complex underlying model. For this purpose, galaxy clustering needs to be simulated accurately, both for the usage of clustering as its own probe and to control systematics. We present a forward model to simulate galaxy surveys, where we extend the Ultra-Fast Image Generator to include galaxy clustering. We use the distribution functions of the galaxy properties, derived from a forward model adjusted to observations. This population model jointly describes the luminosity functions, sizes, ellipticities, SEDs and apparent magnitudes. To simulate the positions of galaxies, we then use a two-parameter relation between galaxies and halos with Subhalo Abundance Matching (SHAM). We simulate the halos and subhalos using the fast PINOCCHIO code, and a method to extract the surviving subhalos from the merger history. Our simulations contain a red and a blue galaxy population, for which we build a SHAM model based on star formation quenching. For central galaxies, mass quenching is controlled with the parameter M$_{\mathrm{limit}}$, with blue galaxies residing in smaller halos. For satellite galaxies, environmental quenching is implemented with the parameter t$_{\mathrm{quench}}$, where blue galaxies occupy only recently merged subhalos. We build and test our model by comparing to imaging data from the Dark Energy Survey Year 1. To ensure completeness in our simulations, we consider the brightest galaxies with $i<20$. We find statistical agreement between our simulations and the data for two-point correlation functions on medium to large scales. Our model provides constraints on the two SHAM parameters M$_{\mathrm{limit}}$ and t$_{\mathrm{quench}}$ and offers great prospects for the quick generation of galaxy mock catalogues, optimized to agree with observations., Comment: Accepted for publication in JCAP. 33 pages, 17 figures

With the rapid advance of wide-field surveys it is increasingly important to perform combined cosmological probe analyses. We present a new pipeline for simulation-based multi-probe analyses, which combines tomographic large-scale structure (LSS) probes (weak lensing and galaxy clustering) with cosmic microwave background (CMB) primary and lensing data. These are combined at the $C_\ell$-level, yielding 12 distinct auto- and cross-correlations. The pipeline is based on $\texttt{UFalconv2}$, a framework to generate fast, self-consistent map-level realizations of cosmological probes from input lightcones, which is applied to the $\texttt{CosmoGridV1}$ N-body simulation suite. It includes a non-Gaussian simulation-based covariance for the LSS tracers, several data compression schemes, and a neural network emulator for accelerated theoretical predictions. We validate our framework, apply it to a simulated $12\times2$pt tomographic analysis of KiDS, BOSS, and $\textit{Planck}$, and forecast constraints for a $\Lambda$CDM model with a variable neutrino mass. We find that, while the neutrino mass constraints are driven by the CMB data, the addition of LSS data helps to break degeneracies and improves the constraint by up to 35%. For a fiducial $M_\nu=0.15\mathrm{eV}$, a full combination of the above CMB+LSS data would enable a $3\sigma$ constraint on the neutrino mass. We explore data compression schemes and find that MOPED outperforms PCA. We also study the impact of an internal lensing tension in the CMB data, parametrized by $A_L$, on the neutrino mass constraint, finding that the addition of LSS to CMB data including all cross-correlations is able to mitigate the impact of this systematic. $\texttt{UFalconv2}$ and a MOPED compressed $\textit{Planck}$ CMB primary + CMB lensing likelihood are made publicly available. [abridged], Comment: Accepted for publication in JCAP. 51 pages including 7 Tables and 17 Figures. Associated $\texttt{UFalconv2}$ code available at https://cosmology.ethz.ch/research/software-lab/UFalcon.html, compressed $\textit{Planck}$ likelihood at https://github.com/alexreevesy/planck_compressed

In recent years, deep learning approaches have achieved state-of-the-art results in the analysis of point cloud data. In cosmology, galaxy redshift surveys resemble such a permutation invariant collection of positions in space. These surveys have so far mostly been analysed with two-point statistics, such as power spectra and correlation functions. The usage of these summary statistics is best justified on large scales, where the density field is linear and Gaussian. However, in light of the increased precision expected from upcoming surveys, the analysis of -- intrinsically non-Gaussian -- small angular separations represents an appealing avenue to better constrain cosmological parameters. In this work, we aim to improve upon two-point statistics by employing a \textit{PointNet}-like neural network to regress the values of the cosmological parameters directly from point cloud data. Our implementation of PointNets can analyse inputs of $\mathcal{O}(10^4) - \mathcal{O}(10^5)$ galaxies at a time, which improves upon earlier work for this application by roughly two orders of magnitude. Additionally, we demonstrate the ability to analyse galaxy redshift survey data on the lightcone, as opposed to previously static simulation boxes at a given fixed redshift.

We present CosmoGridV1: a large set of lightcone simulations for map-level cosmological inference with probes of large scale structure. It is designed for cosmological parameter measurement based on Stage-III photometric surveys with non-Gaussian statistics and machine learning. CosmoGridV1 spans the $w$CDM model by varying $\Omega_m$, $\sigma_8$, $w_0$, $H_0$, $n_s$, $\Omega_b$, and assumes three degenerate neutrinos with $\sum m_\nu$ = 0.06 eV. This space is covered by 2500 grid points on a Sobol sequence. At each grid point, we run 7 simulations with PkdGrav3 and store 69 particle maps at nside=2048 up to $z$=3.5, as well as halo catalog snapshots. The fiducial cosmology has 200 independent simulations, along with their stencil derivatives. An important part of CosmoGridV1 is the benchmark set of 28 simulations, which include larger boxes, higher particle counts, and higher redshift resolution of shells. They allow for testing if new types of analyses are sensitive to choices made in CosmoGridV1. We add baryon feedback effects on the map level, using shell-based baryon correction model. The shells are used to create maps of weak gravitational lensing, intrinsic alignment, and galaxy clustering, using the UFalcon code. The main part of CosmoGridV1 are the raw particle count shells that can be used to create full-sky maps for a given $n(z)$. We also release projected maps for a Stage-III forecast, as well as maps used previously in KiDS-1000 deep learning constraints with CosmoGridV1. The data is available at www.cosmogrid.ai., Comment: Data publicly available at www.cosmogrid.ai

$ $Weak gravitational lensing is a powerful probe which is used to constrain the standard cosmological model and its extensions. With the enhanced statistical precision of current and upcoming surveys, high accuracy predictions for weak lensing statistics are needed to limit the impact of theoretical uncertainties on cosmological parameter constraints. For this purpose, we present a comparison of the theoretical predictions for the nonlinear matter and weak lensing power spectra, based on the widely used fitting functions ($\texttt{mead}$ and $\texttt{rev-halofit}$), emulators ($\texttt{EuclidEmulator}$, $\texttt{EuclidEmulator2}$, $\texttt{BaccoEmulator}$ and $\texttt{CosmicEmulator}$) and N-body simulations ($\texttt{Pkdgrav3}$). We consider the forecasted constraints on the $\Lambda \texttt{CDM}$ and $\texttt{wCDM}$ models from weak lensing for stage III and stage IV surveys. We study the relative bias on the constraints and their dependence on the assumed prescriptions. Assuming a $\Lambda \texttt{CDM}$ cosmology, we find that the relative agreement on the $S_8$ parameter is between $0.2-0.3\sigma$ for a stage III-like survey between the above predictors. For a stage IV-like survey the agreement becomes $1.4-3.0\sigma$. In the $\texttt{wCDM}$ scenario, we find broader $S_8$ constraints, and agreements of $0.18-0.26\sigma$ and $0.7-1.7\sigma$ for stage III and stage IV surveys, respectively. The accuracies of the above predictors therefore appear adequate for stage III surveys, while the fitting functions would need improvements for future stage IV weak lensing surveys. Furthermore, we find that, of the fitting functions, $\texttt{mead}$ provides the best agreement with the emulators. We discuss the implication of these findings for the preparation of the future weak lensing surveys., Comment: 18 pages, 10 figures

Intrinsic alignment (IA) modelling and photometric redshift estimation are two of the main sources of systematic uncertainty in weak lensing surveys. We investigate the impact of redshift errors and their interplay with different IA models. Generally, errors on the mean $\delta_z$ and on the width $\sigma_z$ of the redshift bins can both lead to biases in cosmological constraints. We find that such biases can, however, only be partially resolved by marginalizing over $\delta_z$ and $\sigma_z$. For Stage-III surveys, $\delta_z$ and $\sigma_z$ cannot be well constrained due to limited statistics. The resulting biases are thus sensitive to prior volume effects. For Stage-IV surveys, we observe that marginalizing over the redshift parameters has an impact and reduces the bias. We derive requirements on the uncertainty of $\sigma_z$ and $\delta_z$ for both Stage-III and Stage-IV surveys. We assume that the redshift systematic errors on $S_8$ should be less than half of the statistical errors, and the median bias should be smaller than $0.25\sigma$. We find that the uncertainty on $\delta_z$ has to be $\lesssim0.025$ for the NLA IA model with a Stage-III survey. For $\sigma_z$, the requirement is met even for large uncertainties $\leq0.3$. For the TATT IA model, the uncertainty on $\delta_z$ has to be $\lesssim0.02$ and the uncertainty on $\sigma_z$ has to be $\lesssim0.2$. For Stage-IV surveys, the uncertainty on $\delta_z$ has to be $\lesssim0.005$ and the uncertainty on $\sigma_z$ should be $\lesssim0.1$, with no significant dependence on the IA model. This required high precision will be a challenge for the redshift calibration of these future surveys. Finally, we investigate whether the interplay between redshift systematics and IA modelling can explain the $S_8$-tension between cosmic shear results and CMB measurements. We find that this is unlikely to explain the current $S_8$-tension., Comment: 37 pages including 15 figures and 9 tables, accepted for publication in JCAP

The next generation of weak lensing surveys will measure the matter distribution of the local Universe with unprecedented precision, allowing the resolution of non-Gaussian features of the convergence field. This encourages the use of higher-order mass-map statistics for cosmological parameter inference. We extend the forward-modelling based methodology introduced in a previous forecast paper to match these new requirements. We provide multiple forecasts for the wCDM parameter constraints that can be expected from stage 3 and 4 weak lensing surveys. We consider different survey setups, summary statistics and mass map filters including wavelets. We take into account the shear bias, photometric redshift uncertainties and intrinsic alignment. The impact of baryons is investigated and the necessary scale cuts are applied. We compare the angular power spectrum analysis to peak and minima counts as well as Minkowski functionals of the mass maps. We find a preference for Starlet over Gaussian filters. Our results suggest that using a survey setup with 10 instead of 5 tomographic redshift bins is beneficial. Adding cross-tomographic information improves the constraints on cosmology and especially on galaxy intrinsic alignment for all statistics. In terms of constraining power, we find the angular power spectrum and the peak counts to be equally matched for stage 4 surveys, followed by minima counts and the Minkowski functionals. Combining different summary statistics significantly improves the constraints and compensates the stringent scale cuts. We identify the most `cost-effective' combination to be the angular power spectrum, peak counts and Minkowski functionals following Starlet filtering., Comment: Monthly Notices of the Royal Astronomical Society, 28 July 2023

In classical cosmological analysis of large scale structure surveys with 2-pt functions, the parameter measurement precision is limited by several key degeneracies within the cosmology and astrophysics sectors. For cosmic shear, clustering amplitude $\sigma_8$ and matter density $\Omega_m$ roughly follow the $S_8=\sigma_8(\Omega_m/0.3)^{0.5}$ relation. In turn, $S_8$ is highly correlated with the intrinsic galaxy alignment amplitude $A_{\rm{IA}}$. For galaxy clustering, the bias $b_g$ is degenerate with both $\sigma_8$ and $\Omega_m$, as well as the stochasticity $r_g$. Moreover, the redshift evolution of IA and bias can cause further parameter confusion. A tomographic 2-pt probe combination can partially lift these degeneracies. In this work we demonstrate that a deep learning analysis of combined probes of weak gravitational lensing and galaxy clustering, which we call DeepLSS, can effectively break these degeneracies and yield significantly more precise constraints on $\sigma_8$, $\Omega_m$, $A_{\rm{IA}}$, $b_g$, $r_g$, and IA redshift evolution parameter $\eta_{\rm{IA}}$. The most significant gains are in the IA sector: the precision of $A_{\rm{IA}}$ is increased by approximately 8x and is almost perfectly decorrelated from $S_8$. Galaxy bias $b_g$ is improved by 1.5x, stochasticity $r_g$ by 3x, and the redshift evolution $\eta_{\rm{IA}}$ and $\eta_b$ by 1.6x. Breaking these degeneracies leads to a significant gain in constraining power for $\sigma_8$ and $\Omega_m$, with the figure of merit improved by 15x. We give an intuitive explanation for the origin of this information gain using sensitivity maps. These results indicate that the fully numerical, map-based forward modeling approach to cosmological inference with machine learning may play an important role in upcoming LSS surveys. We discuss perspectives and challenges in its practical deployment for a full survey analysis., Comment: 18 pages, 10 figures, 2 tables, submitted to Physical Review

We present a full forward-modeled $w$CDM analysis of the KiDS-1000 weak lensing maps using graph-convolutional neural networks (GCNN). Utilizing the $\texttt{CosmoGrid}$, a novel massive simulation suite spanning six different cosmological parameters, we generate almost one million tomographic mock surveys on the sphere. Due to the large data set size and survey area, we perform a spherical analysis while limiting our map resolution to $\texttt{HEALPix}$ $n_\mathrm{side}=512$. We marginalize over systematics such as photometric redshift errors, multiplicative calibration and additive shear bias. Furthermore, we use a map-level implementation of the non-linear intrinsic alignment model along with a novel treatment of baryonic feedback to incorporate additional astrophysical nuisance parameters. We also perform a spherical power spectrum analysis for comparison. The constraints of the cosmological parameters are generated using a likelihood free inference method called Gaussian Process Approximate Bayesian Computation (GPABC). Finally, we check that our pipeline is robust against choices of the simulation parameters. We find constraints on the degeneracy parameter of $S_8 \equiv \sigma_8\sqrt{\Omega_M/0.3} = 0.78^{+0.06}_{-0.06}$ for our power spectrum analysis and $S_8 = 0.79^{+0.05}_{-0.05}$ for our GCNN analysis, improving the former by 16%. This is consistent with earlier analyses of the 2-point function, albeit slightly higher. Baryonic corrections generally broaden the constraints on the degeneracy parameter by about 10%. These results offer great prospects for full machine learning based analyses of on-going and future weak lensing surveys., Comment: 22 pages, 13 figures

Large sets of matter density simulations are becoming increasingly important in large-scale structure cosmology. Matter power spectra emulators, such as the Euclid Emulator and CosmicEmu, are trained on simulations to correct the non-linear part of the power spectrum. Map-based analyses retrieve additional non-Gaussian information from the density field, whether through human-designed statistics such as peak counts, or via machine learning methods such as convolutional neural networks. The simulations required for these methods are very resource-intensive, both in terms of computing time and storage. Map-level density field emulators, based on deep generative models, have recently been proposed to address these challenges. In this work, we present a novel mass map emulator of the KiDS-1000 survey footprint, which generates noise-free spherical maps in a fraction of a second. It takes a set of cosmological parameters $(\Omega_M, \sigma_8)$ as input and produces a consistent set of 5 maps, corresponding to the KiDS-1000 tomographic redshift bins. To construct the emulator, we use a conditional generative adversarial network architecture and the spherical CNN $\texttt{DeepSphere}$, and train it on N-body-simulated mass maps. We compare its performance using an array of quantitative comparison metrics: angular power spectra $C_\ell$, pixel/peaks distributions, $C_\ell$ correlation matrices, and Structural Similarity Index. Overall, the average agreement on these summary statistics is $<10\%$ for the cosmologies at the centre of the simulation grid, and degrades slightly on grid edges. Finally, we perform a mock cosmological parameter estimation using the emulator and the original simulation set. We find good agreement in these constraints, for both likelihood and likelihood-free approaches. The emulator is available at https://tfhub.dev/cosmo-group-ethz/models/kids-cgan/1., Comment: 38 pages, 17 figures, 2 tables. Link to software: https://tfhub.dev/cosmo-group-ethz/models/kids-cgan/1

The analysis of cosmological galaxy surveys requires realistic simulations for their interpretation. Forward modelling is a powerful method to simulate galaxy clustering without the need for an underlying complex model. This approach requires fast cosmological simulations with a high resolution and large volume, to resolve small dark matter halos associated to single galaxies. In this work, we present fast halo and subhalo clustering simulations based on the Lagrangian perturbation theory code PINOCCHIO, which generates halos and merger trees. The subhalo progenitors are extracted from the merger history and the survival of subhalos is modelled. We introduce a new fitting function for the subhalo merger time, which includes a redshift dependence of the fitting parameters. The spatial distribution of subhalos within their hosts is modelled using a number density profile. We compare our simulations with the halo finder ROCKSTAR applied to the full N-body code GADGET-2. The subhalo velocity function and the correlation function of halos and subhalos are in good agreement. We investigate the effect of the chosen number density profile on the resulting subhalo clustering. Our simulation is approximate yet realistic and significantly faster compared to a full N-body simulation combined with a halo finder. The fast halo and subhalo clustering simulations offer good prospects for galaxy forward models using subhalo abundance matching., Comment: 28 pages, 10 figures, Accepted for publication in JCAP

The ability to obtain reliable point estimates of model parameters is of crucial importance in many fields of physics. This is often a difficult task given that the observed data can have a very high number of dimensions. In order to address this problem, we propose a novel approach to construct parameter estimators with a quantifiable bias using an order expansion of highly compressed deep summary statistics of the observed data. These summary statistics are learned automatically using an information maximising loss. Given an observation, we further show how one can use the constructed estimators to obtain approximate Bayes computation (ABC) posterior estimates and their corresponding uncertainties that can be used for parameter inference using Gaussian process regression even if the likelihood is not tractable. We validate our method with an application to the problem of cosmological parameter inference of weak lensing mass maps. We show in that case that the constructed estimators are unbiased and have an almost optimal variance, while the posterior distribution obtained with the Gaussian process regression is close to the true posterior and performs better or equally well than comparable methods., Comment: 18 pages, 10 figures

Narrow-band imaging surveys allow the study of the spectral characteristics of galaxies without the need of performing their spectroscopic follow-up. In this work, we forward-model the Physics of the Accelerating Universe Survey (PAUS) narrow-band data. The aim is to improve the constraints on the spectral coefficients used to create the galaxy spectral energy distributions (SED) of the galaxy population model in Tortorelli et al. 2020. In that work, the model parameters were inferred from the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) data using Approximate Bayesian Computation (ABC). This led to stringent constraints on the B-band galaxy luminosity function parameters, but left the spectral coefficients only broadly constrained. To address that, we perform an ABC inference using CFHTLS and PAUS data. This is the first time our approach combining forward-modelling and ABC is applied simultaneously to multiple datasets. We test the results of the ABC inference by comparing the narrow-band magnitudes of the observed and simulated galaxies using Principal Component Analysis, finding a very good agreement. Furthermore, we prove the scientific potential of the constrained galaxy population model to provide realistic stellar population properties by measuring them with the SED fitting code \textsc{CIGALE}. We use CFHTLS broad-band and PAUS narrow-band photometry for a flux-limited ($\mathrm{i}<22.5$) sample of galaxies up to redshift $\mathrm{z \sim 0.8}$. We find that properties like stellar masses, star-formation rates, mass-weighted stellar ages and metallicities are in agreement within errors between observations and simulations. Overall, this work shows the ability of our galaxy population model to correctly forward-model a complex dataset such as PAUS and the ability to reproduce the diversity of galaxy properties at the redshift range spanned by CFHTLS and PAUS., Comment: 53 pages, 17 figures, Accepted for publication in JCAP

The combination of different cosmological probes offers stringent tests of the $\Lambda$CDM model and enhanced control of systematics. For this purpose, we present an extension of the lightcone generator UFalcon first introduced in Sgier et al. 2019 (arXiv:1801.05745), enabling the simulation of a self-consistent set of maps for different cosmological probes. Each realization is generated from the same underlying simulated density field, and contains full-sky maps of different probes, namely weak lensing shear, galaxy overdensity including RSD, CMB lensing, and CMB temperature anisotropies from the ISW effect. The lightcone generation performed by UFalcon is parallelized and based on the replication of a large periodic volume simulated with the GPU-accelerated $N$-Body code PkdGrav3. The post-processing to construct the lightcones requires only a runtime of about 1 walltime-hour corresponding to about 100 CPU-hours. We use a randomization procedure to increase the number of quasi-independent full-sky UFalcon map-realizations, which enables us to compute an accurate multi-probe covariance matrix. Using this framework, we forecast cosmological parameter constraints by performing a multi-probe likelihood analysis for a combination of simulated future stage-IV-like surveys. We find that the inclusion of the cross-correlations between the probes significantly increases the information gain in the parameter constraints. We also find that the use of a non-Gaussian covariance matrix is increasingly important, as more probes and cross-correlation power spectra are included. A version of the UFalcon package currently including weak gravitational lensing is publicly available., Comment: 49 pages, 24 pictures, The UFalcon weak lensing package is available here: $\href{https://cosmology.ethz.ch/research/software-lab/UFalcon.html}{https://cosmology.ethz.ch/research/software-lab/UFalcon.html}$

Cosmic shear data contains a large amount of cosmological information encapsulated in the non-Gaussian features of the weak lensing mass maps. This information can be extracted using non-Gaussian statistics. We compare the constraining power in the $\Omega_{\mathrm{m}} - \sigma_8$ plane of three map-based non-Gaussian statistics with the angular power spectrum, namely; peak/minimum counts and Minkowski functionals. We further analyze the impact of tomography and systematic effects originating from galaxy intrinsic alignments, multiplicative shear bias and photometric redshift systematics. We forecast the performance of the statistics for a stage-3-like weak lensing survey and restrict ourselves to scales $\geq$ 10 arcmin. We find, that in our setup, the considered non-Gaussian statistics provide tighter constraints than the angular power spectrum. The peak counts show the greatest potential, increasing the Figure-of-Merit (FoM) in the $\Omega_{\mathrm{m}} - \sigma_8$ plane by a factor of about 4. A combined analysis using all non-Gaussian statistics in addition to the power spectrum increases the FoM by a factor of 5 and reduces the error on $S_8$ by $\approx$ 25\%. We find that the importance of tomography is diminished when combining non-Gaussian statistics with the angular power spectrum. The non-Gaussian statistics indeed profit less from tomography and the minimum counts and Minkowski functionals add some robustness against galaxy intrinsic alignment in a non-tomographic setting. We further find that a combination of the angular power spectrum and the non-Gaussian statistics allows us to apply conservative scale cuts in the analysis, thus helping to minimize the impact of baryonic and relativistic effects, while conserving the cosmological constraining power. We make the code that was used to conduct this analysis publicly available.

Weak gravitational lensing mass maps play a crucial role in understanding the evolution of structures in the universe and our ability to constrain cosmological models. The prediction of these mass maps is based on expensive N-body simulations, which can create a computational bottleneck for cosmological analyses. Modern deep generative models, such as Generative Adversarial Networks (GAN), have demonstrated their potential to achieve this goal. Most existing GAN approaches produce simulations for a fixed value of the cosmological parameters, which limits their practical applicability. We propose a novel conditional GAN model that is able to generate mass maps for any pair of matter density $\Omega_m$ and matter clustering strength $\sigma_8$, parameters which have the largest impact on the evolution of structures in the universe. Our results show that our conditional GAN can interpolate efficiently within the space of simulated cosmologies, and generate maps anywhere inside this space with good visual quality high statistical accuracy. We perform an extensive quantitative comparison of the N-body and GAN -generated maps using a range of metrics: the pixel histograms, peak counts, power spectra, bispectra, Minkowski functionals, correlation matrices of the power spectra, the Multi-Scale Structural Similarity Index (MS-SSIM) and our equivalent of the Fr\'echet Inception Distance (FID). We find a very good agreement on these metrics, with typical differences are <5% at the centre of the simulation grid, and slightly worse for cosmologies at the grid edges. The agreement for the bispectrum is slightly worse, on the <20% level. This contribution is a step towards building emulators of mass maps directly, capturing both the cosmological signal and its variability. We make the code and the data publicly available: https://renkulab.io/gitlab/nathanael.perraudin/darkmattergan, Comment: Accepted at the Workshop at the 33rd Conference on Neural Information Processing Systems (NeurIPS), December 14, 2019, https://ml4physicalsciences.github.io/files/NeurIPS_ML4PS_2019_97.pdf Accepted in Frontiers in Artificial Intelligence in May 2021

The galaxy Luminosity Function (LF) is a key observable for galaxy formation, evolution studies and for cosmology. In this work, we propose a novel technique to forward model wide-field broad-band galaxy surveys using the fast image simulator UFig and measure the LF of galaxies in the B-band. We use Approximate Bayesian Computation (ABC) to constrain the galaxy population model parameters of the simulations and match data from CFHTLS. We define a number of distance metrics between the simulated and the survey data. By exploring the parameter space of the galaxy population model through ABC to find the set of parameters that minimize these distance metrics, we obtain constraints on the LFs of blue and red galaxies as a function of redshift. We find that $\mathrm{M^*}$ fades by $\Delta \mathrm{M}^*_{\mathrm{0.1-1.0,b}} = 0.68 \pm 0.52$ and $\Delta \mathrm{M}^*_{\mathrm{0.1-1.0,r}} = 0.54 \pm 0.48$ magnitudes between redshift $\mathrm{z = 1}$ and $\mathrm{z = 0.1}$ for blue and red galaxies, respectively. We also find that $\phi^*$ for blue galaxies stays roughly constant between redshift $\mathrm{z = 0.1}$ and $\mathrm{z=1}$, while for red galaxies it decreases by $\sim 35\%$. We compare our results to other measurements, finding good agreement at all redshifts, for both blue and red galaxies. To further test our results, we compare the redshift distributions for survey and simulated data. We use the spectroscopic redshift distribution from the VIMOS Public Extragalactic Redshift Survey (VIPERS) and we apply the same selection in colours and magnitudes on our simulations. We find a good agreement between the survey and the simulated redshift distributions. We provide best-fit values and uncertainties for the parameters of the LF. This work offers excellent prospects for measuring other galaxy population properties as a function of redshift using ABC., Comment: Accepted for publication in JCAP, 44 pages, 20 figures, 4 appendices

An accurate modelling of baryonic feedback effects is required to exploit the full potential of future weak-lensing surveys such as Euclid or LSST. In this second paper in a series of two, we combine Euclid-like mock data of the cosmic shear power spectrum with an eROSITA X-ray mock of the cluster gas fraction to run a combined likelihood analysis including both cosmological and baryonic parameters. Following the first paper of this series, the baryonic effects (based on the baryonic correction model of Schneider et al. 2019) are included in both the tomographic power spectrum and the covariance matrix. However, this time we assume the more realistic case of a $\Lambda$CDM cosmology with massive neutrinos, and we consider several extensions of the currently favoured cosmological model. For the standard $\Lambda$CDM case, we show that including X-ray data reduces the uncertainties on the sum of the neutrino mass by $\sim30$ percent, while there is only a mild improvement on other parameters such as $\Omega_m$ and $\sigma_8$. As extensions of $\Lambda$CDM, we consider the cases of a dynamical dark energy model (wCDM), a $f(R)$ gravity model (fRCDM), and a mixed dark matter model ($\Lambda$MDM) with both a cold and a warm/hot dark matter component. We find that combining weak lensing with X-ray data only leads to a mild improvement of the constraints on the additional parameters of wCDM, while the improvement is more substantial for both fRCDM and $\Lambda$MDM. Ignoring baryonic effects in the analysis pipeline leads to significant false-detections of either phantom dark energy or a light subdominant dark matter component. Overall we conclude that for all cosmologies considered, a general parametrisation of baryonic effects is both necessary and sufficient to obtain tight constraints on cosmological parameters., Comment: Accepted version (JCAP)

Deep generative models, such as Generative Adversarial Networks (GANs) or Variational Autoencoders (VAs) have been demonstrated to produce images of high visual quality. However, the existing hardware severely limits the size of the images that can be generated. The rapid growth of high dimensional data in many fields of science therefore poses a significant challenge for generative models. In cosmology, the large-scale, three-dimensional matter distribution, modeled with N-body simulations, plays a crucial role in understanding the evolution of the universe. As these simulations are computationally very expensive, GANs have recently generated interest as a possible method to emulate these datasets, but they have been, so far, mostly limited to two dimensional data. In this work, we introduce a new benchmark for the generation of three dimensional N-body simulations, in order to stimulate new ideas in the machine learning community and move closer to the practical use of generative models in cosmology. As a first benchmark result, we propose a scalable GAN approach for training a generator of N-body three-dimensional cubes. Our technique relies on two key building blocks, (i) splitting the generation of the high-dimensional data into smaller parts, and (ii) using a multi-scale approach that efficiently captures global image features that might otherwise be lost in the splitting process. We evaluate the performance of our model for the generation of N-body samples using various statistical measures commonly used in cosmology. Our results show that the proposed model produces samples of high visual quality, although the statistical analysis reveals that capturing rare features in the data poses significant problems for the generative models. We make the data, quality evaluation routines, and the proposed GAN architecture publicly available at https://github.com/nperraud/3DcosmoGAN

Convolutional Neural Networks (CNN) have recently been demonstrated on synthetic data to improve upon the precision of cosmological inference. In particular they have the potential to yield more precise cosmological constraints from weak lensing mass maps than the two-point functions. We present the cosmological results with a CNN from the KiDS-450 tomographic weak lensing dataset, constraining the total matter density $\Omega_m$, the fluctuation amplitude $\sigma_8$, and the intrinsic alignment amplitude $A_{\rm{IA}}$. We use a grid of N-body simulations to generate a training set of tomographic weak lensing maps. We test the robustness of the expected constraints to various effects, such as baryonic feedback, simulation accuracy, different value of $H_0$, or the lightcone projection technique. We train a set of ResNet-based CNNs with varying depths to analyze sets of tomographic KiDS mass maps divided into 20 flat regions, with applied Gaussian smoothing of $\sigma=2.34$ arcmin. The uncertainties on shear calibration and $n(z)$ error are marginalized in the likelihood pipeline. Following a blinding scheme, we derive constraints of $S_8 = \sigma_8 (\Omega_m/0.3)^{0.5} = 0.777^{+0.038}_{-0.036}$ with our CNN analysis, with $A_{\rm{IA}}=1.398^{+0.779}_{-0.724}$. We compare this result to the power spectrum analysis on the same maps and likelihood pipeline and find an improvement of about $30\%$ for the CNN. We discuss how our results offer excellent prospects for the use of deep learning in future cosmological data analysis., Comment: 22 pages, 15 figures

Upcoming weak-lensing surveys have the potential to become leading cosmological probes provided all systematic effects are under control. Recently, the ejection of gas due to feedback energy from active galactic nuclei (AGN) has been identified as major source of uncertainty, challenging the success of future weak-lensing probes in terms of cosmology. In this paper we investigate the effects of baryons on the number of weak-lensing peaks in the convergence field. Our analysis is based on full-sky convergence maps constructed via light-cones from $N$-body simulations, and we rely on the baryonic correction model of Schneider et al. (2019) to model the baryonic effects on the density field. As a result we find that the baryonic effects strongly depend on the Gaussian smoothing applied to the convergence map. For a DES-like survey setup, a smoothing of $\theta_k\gtrsim8$ arcmin is sufficient to keep the baryon signal below the expected statistical error. Smaller smoothing scales lead to a significant suppression of high peaks (with signal-to-noise above 2), while lower peaks are not affected. The situation is more severe for a Euclid-like setup, where a smoothing of $\theta_k\gtrsim16$ arcmin is required to keep the baryonic suppression signal below the statistical error. Smaller smoothing scales require a full modelling of baryonic effects since both low and high peaks are strongly affected by baryonic feedback., Comment: 22 pages, 11 figures, JCAP accepted

Spherical data is found in many applications. By modeling the discretized sphere as a graph, we can accommodate non-uniformly distributed, partial, and changing samplings. Moreover, graph convolutions are computationally more efficient than spherical convolutions. As equivariance is desired to exploit rotational symmetries, we discuss how to approach rotation equivariance using the graph neural network introduced in Defferrard et al. (2016). Experiments show good performance on rotation-invariant learning problems. Code and examples are available at https://github.com/SwissDataScienceCenter/DeepSphere, Comment: published at the ICLR 2019 Workshop on Representation Learning on Graphs and Manifolds. arXiv admin note: text overlap with arXiv:1810.12186

Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those supporting images, audio, or video. Because of their success, CNN-based methods are becoming increasingly popular in Cosmology. Cosmological data often comes as spherical maps, which make the use of the traditional CNNs more complicated. The commonly used pixelization scheme for spherical maps is the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for analysis of full and partial HEALPix maps, which we call DeepSphere. The spherical CNN is constructed by representing the sphere as a graph. Graphs are versatile data structures that can act as a discrete representation of a continuous manifold. Using the graph-based representation, we define many of the standard CNN operations, such as convolution and pooling. With filters restricted to being radial, our convolutions are equivariant to rotation on the sphere, and DeepSphere can be made invariant or equivariant to rotation. This way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix sampling of the sphere. This approach is computationally more efficient than using spherical harmonics to perform convolutions. We demonstrate the method on a classification problem of weak lensing mass maps from two cosmological models and compare the performance of the CNN with that of two baseline classifiers. The results show that the performance of DeepSphere is always superior or equal to both of these baselines. For high noise levels and for data covering only a smaller fraction of the sphere, DeepSphere achieves typically 10% better classification accuracy than those baselines. Finally, we show how learned filters can be visualized to introspect the neural network., Comment: arXiv admin note: text overlap with arXiv:astro-ph/0409513 by other authors

Deep learning is a powerful analysis technique that has recently been proposed as a method to constrain cosmological parameters from weak lensing mass maps. Due to its ability to learn relevant features from the data, it is able to extract more information from the mass maps than the commonly used power spectrum, and thus achieve better precision for cosmological parameter measurement. We explore the advantage of Convolutional Neural Networks (CNN) over the power spectrum for varying levels of shape noise and different smoothing scales applied to the maps. We compare the cosmological constraints from the two methods in the $\Omega_M-\sigma_8$ plane for sets of 400 deg$^2$ convergence maps. We find that, for a shape noise level corresponding to 8.53 galaxies/arcmin$^2$ and the smoothing scale of $\sigma_s = 2.34$ arcmin, the network is able to generate 45% tighter constraints. For smaller smoothing scale of $\sigma_s = 1.17$ the improvement can reach $\sim 50 \%$, while for larger smoothing scale of $\sigma_s = 5.85$, the improvement decreases to 19%. The advantage generally decreases when the noise level and smoothing scales increase. We present a new training strategy to train the neural network with noisy data, as well as considerations for practical applications of the deep learning approach., Comment: 17 pages, 12 figures

Weak lensing peak counts are a powerful statistical tool for constraining cosmological parameters. So far, this method has been applied only to surveys with relatively small areas, up to several hundred square degrees. As future surveys will provide weak lensing datasets with size of thousands of square degrees, the demand on the theoretical prediction of the peak statistics will become heightened. In particular, large simulations of increased cosmological volume are required. In this work, we investigate the possibility of using simulations generated with the fast Comoving-Lagrangian acceleration (COLA) method, coupled to the convergence map generator Ufalcon, for predicting the peak counts. We examine the systematics introduced by the COLA method by comparing it with a full TreePM code. We find that for a 2000 deg$^2$ survey, the systematic error is much smaller than the statistical error. This suggests that the COLA method is able to generate promising theoretical predictions for weak lensing peaks. We also examine the constraining power of various configurations of data vectors, exploring the influence of splitting the sample into tomographic bins and combining different smoothing scales. We find the combination of smoothing scales to have the most constraining power, improving the constraints on the $S_8$ amplitude parameter by at least 40% compared to a single smoothing scale, with tomography brining only limited increase in measurement precision., Comment: 17 pages, 9 figures

Dark matter in the universe evolves through gravity to form a complex network of halos, filaments, sheets and voids, that is known as the cosmic web. Computational models of the underlying physical processes, such as classical N-body simulations, are extremely resource intensive, as they track the action of gravity in an expanding universe using billions of particles as tracers of the cosmic matter distribution. Therefore, upcoming cosmology experiments will face a computational bottleneck that may limit the exploitation of their full scientific potential. To address this challenge, we demonstrate the application of a machine learning technique called Generative Adversarial Networks (GAN) to learn models that can efficiently generate new, physically realistic realizations of the cosmic web. Our training set is a small, representative sample of 2D image snapshots from N-body simulations of size 500 and 100 Mpc. We show that the GAN-generated samples are qualitatively and quantitatively very similar to the originals. For the larger boxes of size 500 Mpc, it is very difficult to distinguish them visually. The agreement of the power spectrum $P_k$ is 1-2\% for most of the range, between $k=0.06$ and $k=0.4$. An important advantage of generating cosmic web realizations with a GAN is the considerable gains in terms of computation time. Each new sample generated by a GAN takes a fraction of a second, compared to the many hours needed by traditional N-body techniques. We anticipate that the use of generative models such as GANs will therefore play an important role in providing extremely fast and precise simulations of cosmic web in the era of large cosmological surveys, such as Euclid and Large Synoptic Survey Telescope (LSST).

Modeling the Point Spread Function (PSF) of wide-field surveys is vital for many astrophysical applications and cosmological probes including weak gravitational lensing. The PSF smears the image of any recorded object and therefore needs to be taken into account when inferring properties of galaxies from astronomical images. In the case of cosmic shear, the PSF is one of the dominant sources of systematic errors and must be treated carefully to avoid biases in cosmological parameters. Recently, forward modeling approaches to calibrate shear measurements within the Monte-Carlo Control Loops ($MCCL$) framework have been developed. These methods typically require simulating a large amount of wide-field images, thus, the simulations need to be very fast yet have realistic properties in key features such as the PSF pattern. Hence, such forward modeling approaches require a very flexible PSF model, which is quick to evaluate and whose parameters can be estimated reliably from survey data. We present a PSF model that meets these requirements based on a fast deep-learning method to estimate its free parameters. We demonstrate our approach on publicly available SDSS data. We extract the most important features of the SDSS sample via principal component analysis. Next, we construct our model based on perturbations of a fixed base profile, ensuring that it captures these features. We then train a Convolutional Neural Network to estimate the free parameters of the model from noisy images of the PSF. This allows us to render a model image of each star, which we compare to the SDSS stars to evaluate the performance of our method. We find that our approach is able to accurately reproduce the SDSS PSF at the pixel level, which, due to the speed of both the model evaluation and the parameter estimation, offers good prospects for incorporating our method into the $MCCL$ framework., Comment: 25 pages, 8 figures, 1 table

Approximate Bayesian Computation (ABC) is a method to obtain a posterior distribution without a likelihood function, using simulations and a set of distance metrics. For that reason, it has recently been gaining popularity as an analysis tool in cosmology and astrophysics. Its drawback, however, is a slow convergence rate. We propose a novel method, which we call qABC, to accelerate ABC with Quantile Regression. In this method, we create a model of quantiles of distance measure as a function of input parameters. This model is trained on a small number of simulations and estimates which regions of the prior space are likely to be accepted into the posterior. Other regions are then immediately rejected. This procedure is then repeated as more simulations are available. We apply it to the practical problem of estimation of redshift distribution of cosmological samples, using forward modelling developed in previous work. The qABC method converges to nearly same posterior as the basic ABC. It uses, however, only 20\% of the number of simulations compared to basic ABC, achieving a fivefold gain in execution time for our problem. For other problems the acceleration rate may vary; it depends on how close the prior is to the final posterior. We discuss possible improvements and extensions to this method., Comment: 10 pages, 5 figures, prepared for submission to JCAP

Weak Gravitational Lensing is a powerful probe of the dark sector of the Universe. One of the main challenges for this technique is the treatment of systematics in the measurement of cosmic shear from galaxy shapes. In an earlier work, Refregier & Amara (2014) have proposed the Monte Carlo Control Loops (MCCL) to overcome these effects using a forward modeling approach. We focus here on one of the control loops in this method, the task of which is the calibration of the shear measurement. For this purpose, we first consider the requirements on the shear systematics for a given survey and propagate them to different systematics terms. We use two one-point statistics to calibrate the shear measurement and six further one-point statistics as diagnostics. We also propagate the systematics levels that we estimate from the one-point functions to the two-point functions for the different systematic error sources. This allows us to assess the consistency between the systematics levels measured in different ways. To test the method, we construct synthetic sky surveys with an area of 1,700 deg$^2$. With some simplifying assumptions, we are able to meet the requirements on the shear calibration for this survey configuration. Furthermore, we account for the total residual shear systematics in terms of the contributing sources. We discuss how this MCCL framework can be applied to current and future weak lensing surveys., Comment: 23 pages, 4 figures, prepared for submission to JCAP

We demonstrate the potential of Deep Learning methods for measurements of cosmological parameters from density fields, focusing on the extraction of non-Gaussian information. We consider weak lensing mass maps as our dataset. We aim for our method to be able to distinguish between five models, which were chosen to lie along the $\sigma_8$ - $\Omega_m$ degeneracy, and have nearly the same two-point statistics. We design and implement a Deep Convolutional Neural Network (DCNN) which learns the relation between five cosmological models and the mass maps they generate. We develop a new training strategy which ensures the good performance of the network for high levels of noise. We compare the performance of this approach to commonly used non-Gaussian statistics, namely the skewness and kurtosis of the convergence maps. We find that our implementation of DCNN outperforms the skewness and kurtosis statistics, especially for high noise levels. The network maintains the mean discrimination efficiency greater than $85\%$ even for noise levels corresponding to ground based lensing observations, while the other statistics perform worse in this setting, achieving efficiency less than $70\%$. This demonstrates the ability of CNN-based methods to efficiently break the $\sigma_8$ - $\Omega_m$ degeneracy with weak lensing mass maps alone. We discuss the potential of this method to be applied to the analysis of real weak lensing data and other datasets., Comment: 21 pages, 9 figures, prepared for submission to JCAP

Determining the redshift distribution $n(z)$ of galaxy samples is essential for several cosmological probes including weak lensing. For imaging surveys, this is usually done using photometric redshifts estimated on an object-by-object basis. We present a new approach for directly measuring the global $n(z)$ of cosmological galaxy samples, including uncertainties, using forward modeling. Our method relies on image simulations produced using UFig (Ultra Fast Image Generator) and on ABC (Approximate Bayesian Computation) within the $MCCL$ (Monte-Carlo Control Loops) framework. The galaxy population is modeled using parametric forms for the luminosity functions, spectral energy distributions, sizes and radial profiles of both blue and red galaxies. We apply exactly the same analysis to the real data and to the simulated images, which also include instrumental and observational effects. By adjusting the parameters of the simulations, we derive a set of acceptable models that are statistically consistent with the data. We then apply the same cuts to the simulations that were used to construct the target galaxy sample in the real data. The redshifts of the galaxies in the resulting simulated samples yield a set of $n(z)$ distributions for the acceptable models. We demonstrate the method by determining $n(z)$ for a cosmic shear like galaxy sample from the 4-band Subaru Suprime-Cam data in the COSMOS field. We also complement this imaging data with a spectroscopic calibration sample from the VVDS survey. We compare our resulting posterior $n(z)$ distributions to the one derived from photometric redshifts estimated using 36 photometric bands in COSMOS and find good agreement. This offers good prospects for applying our approach to current and future large imaging surveys., Comment: 26 pages, 10 figures

We use wavelet and curvelet transforms to extract signals of cosmic strings from cosmic microwave background (CMB) temperature anisotropy maps, and to study the limits on the cosmic string tension which various ongoing CMB temperature anisotropy experiments will be able to achieve. We construct sky maps with size and angular resolution corresponding to various experiments. These maps contain the signals of a scaling solution of long string segments with a given string tension $G \mu$, the contribution of the dominant Gaussian primordial cosmological fluctuations, and pixel by pixel white noise with an amplitude corresponding to the instrumental noise of the various experiments. In the case that we include white noise, we find that the curvelets are more powerful than wavelets. For maps with Planck specification, we obtain bounds on the string tension comparable to what was obtained by the Planck collaboration. Experiments with better angular resolution such as the South Pole Telescope third generation (SPT-3G) survey will be able to yield stronger limits. For maps with a specification of SPT-3G we find that string signals will be visible down to a string tension of $G \mu = 1.4 \times 10^{-7}$., Comment: 13 pages, 7 figures, 3 tables

We present cosmological constraints from the Dark Energy Survey (DES) using a combined analysis of angular clustering of red galaxies and their cross-correlation with weak gravitational lensing of background galaxies. We use a 139 square degree contiguous patch of DES data from the Science Verification (SV) period of observations. Using large scale measurements, we constrain the matter density of the Universe as Omega_m = 0.31 +/- 0.09 and the clustering amplitude of the matter power spectrum as sigma_8 = 0.74 +/- 0.13 after marginalizing over seven nuisance parameters and three additional cosmological parameters. This translates into S_8 = sigma_8(Omega_m/0.3)^{0.16} = 0.74 +/- 0.12 for our fiducial lens redshift bin at 0.35

We present first results from the third GRavitational lEnsing Accuracy Testing (GREAT3) challenge, the third in a sequence of challenges for testing methods of inferring weak gravitational lensing shear distortions from simulated galaxy images. GREAT3 was divided into experiments to test three specific questions, and included simulated space- and ground-based data with constant or cosmologically-varying shear fields. The simplest (control) experiment included parametric galaxies with a realistic distribution of signal-to-noise, size, and ellipticity, and a complex point spread function (PSF). The other experiments tested the additional impact of realistic galaxy morphology, multiple exposure imaging, and the uncertainty about a spatially-varying PSF; the last two questions will be explored in Paper II. The 24 participating teams competed to estimate lensing shears to within systematic error tolerances for upcoming Stage-IV dark energy surveys, making 1525 submissions overall. GREAT3 saw considerable variety and innovation in the types of methods applied. Several teams now meet or exceed the targets in many of the tests conducted (to within the statistical errors). We conclude that the presence of realistic galaxy morphology in simulations changes shear calibration biases by $\sim 1$ per cent for a wide range of methods. Other effects such as truncation biases due to finite galaxy postage stamps, and the impact of galaxy type as measured by the S\'{e}rsic index, are quantified for the first time. Our results generalize previous studies regarding sensitivities to galaxy size and signal-to-noise, and to PSF properties such as seeing and defocus. Almost all methods' results support the simple model in which additive shear biases depend linearly on PSF ellipticity., Comment: 32 pages + 15 pages of technical appendices; 28 figures; published in MNRAS; all data and other information may be found at https://github.com/barnabytprowe/great3-public as the GREAT3 website and leaderboard are no longer live. v3 has updates to this comment only

GALSIM is a collaborative, open-source project aimed at providing an image simulation tool of enduring benefit to the astronomical community. It provides a software library for generating images of astronomical objects such as stars and galaxies in a variety of ways, efficiently handling image transformations and operations such as convolution and rendering at high precision. We describe the GALSIM software and its capabilities, including necessary theoretical background. We demonstrate that the performance of GALSIM meets the stringent requirements of high precision image analysis applications such as weak gravitational lensing, for current datasets and for the Stage IV dark energy surveys of the Large Synoptic Survey Telescope, ESA's Euclid mission, and NASA's WFIRST-AFTA mission. The GALSIM project repository is public and includes the full code history, all open and closed issues, installation instructions, documentation, and wiki pages (including a Frequently Asked Questions section). The GALSIM repository can be found at https://github.com/GalSim-developers/GalSim ., Comment: 38 pages, 3 tables, 8 figures, accepted for publication in Astronomy & Computing

The GRavitational lEnsing Accuracy Testing 3 (GREAT3) challenge is the third in a series of image analysis challenges, with a goal of testing and facilitating the development of methods for analyzing astronomical images that will be used to measure weak gravitational lensing. This measurement requires extremely precise estimation of very small galaxy shape distortions, in the presence of far larger intrinsic galaxy shapes and distortions due to the blurring kernel caused by the atmosphere, telescope optics, and instrumental effects. The GREAT3 challenge is posed to the astronomy, machine learning, and statistics communities, and includes tests of three specific effects that are of immediate relevance to upcoming weak lensing surveys, two of which have never been tested in a community challenge before. These effects include realistically complex galaxy models based on high-resolution imaging from space; spatially varying, physically-motivated blurring kernel; and combination of multiple different exposures. To facilitate entry by people new to the field, and for use as a diagnostic tool, the simulation software for the challenge is publicly available, though the exact parameters used for the challenge are blinded. Sample scripts to analyze the challenge data using existing methods will also be provided. See http://great3challenge.info and http://great3.projects.phys.ucl.ac.uk/leaderboard/ for more information., Comment: 30 pages, 13 figures, published in MNRAS. URLs in abstract no longer work, but all data are available for download as described in https://github.com/barnabytprowe/great3-public (v4 only has updates to comments)

Cosmic shear is a powerful probe of cosmological parameters, but its potential can be fully utilised only if galaxy shapes are measured with great accuracy. Two major effects have been identified which are likely to account for most of the bias for maximum likelihood methods in recent shear measurement challenges. Model bias occurs when the true galaxy shape is not well represented by the fitted model. Noise bias occurs due to the non-linear relationship between image pixels and galaxy shape. In this paper we investigate the potential interplay between these two effects when an imperfect model is used in the presence of high noise. We present analytical expressions for this bias, which depends on the residual difference between the model and real data. They can lead to biases not accounted for in previous calibration schemes. By measuring the model bias, noise bias and their interaction, we provide a complete statistical framework for measuring galaxy shapes with model fitting methods from GRavitational lEnsing Accuracy Testing (GREAT) like images. We demonstrate the noise and model interaction bias using a simple toy model, which indicates that this effect can potentially be significant. Using real galaxy images from the Cosmological Evolution Survey (COSMOS) we quantify the strength of the model bias, noise bias and their interaction. We find that the interaction term is often a similar size to the model bias term, and is smaller than the requirements of the current and shortly upcoming galaxy surveys., Comment: 11 pages, 3 figures

We present and describe im3shape, a new publicly available galaxy shape measurement code for weak gravitational lensing shear. im3shape performs a maximum likelihood fit of a bulge-plus-disc galaxy model to noisy images, incorporating an applied point spread function. We detail challenges faced and choices made in its design and implementation, and then discuss various limitations that affect this and other maximum likelihood methods. We assess the bias arising from fitting an incorrect galaxy model using simple noise-free images and find that it should not be a concern for current cosmic shear surveys. We test im3shape on the GREAT08 Challenge image simulations, and meet the requirements for upcoming cosmic shear surveys in the case that the simulations are encompassed by the fitted model, using a simple correction for image noise bias. For the fiducial branch of GREAT08 we obtain a negligible additive shear bias and sub-two percent level multiplicative bias, which is suitable for analysis of current surveys. We fall short of the sub-percent level requirement for upcoming surveys, which we attribute to a combination of noise bias and the mis-match between our galaxy model and the model used in the GREAT08 simulations. We meet the requirements for current surveys across all branches of GREAT08, except those with small or high noise galaxies, which we would cut from our analysis. Using the GREAT08 metric we we obtain a score of Q=717 for the usable branches, relative to the goal of Q=1000 for future experiments. The code is freely available from https://bitbucket.org/joezuntz/im3shape, Comment: 16 pages including appendices. Figure 8 is the money plot

Weak lensing experiments are a powerful probe of cosmology through their measurement of the mass distribution of the universe. A challenge for this technique is to control systematic errors that occur when measuring the shapes of distant galaxies. In this paper we investigate noise bias, a systematic error that arises from second order noise terms in the shape measurement process. We first derive analytical expressions for the bias of general Maximum Likelihood Estimators (MLEs) in the presence of additive noise. We then find analytical expressions for a simplified toy model in which galaxies are modeled and fitted with a Gaussian with its size as a single free parameter. Even for this very simple case we find a significant effect. We also extend our analysis to a more realistic 6-parameter elliptical Gaussian model. We find that the noise bias is generically of the order of the inverse-squared signal-to-noise ratio (SNR) of the galaxies and is thus of the order of a percent for galaxies of SNR of 10, i.e. comparable to the weak lensing shear signal. This is nearly two orders of magnitude greater than the systematics requirements for future all-sky weak lensing surveys. We discuss possible ways to circumvent this effect, including a calibration method using simulations discussed in an associated paper., Comment: 8 pages, 3 figures, submitted to MNRAS

Weak gravitational lensing has the potential to constrain cosmological parameters to high precision. However, as shown by the Shear TEsting Programmes (STEP) and GRavitational lEnsing Accuracy Testing (GREAT) Challenges, measuring galaxy shears is a nontrivial task: various methods introduce different systematic biases which have to be accounted for. We investigate how pixel noise on the image affects the bias on shear estimates from a Maximum-Likelihood forward model-fitting approach using a sum of co-elliptical S\'{e}rsic profiles, in complement to the theoretical approach of an an associated paper. We evaluate the bias using a simple but realistic galaxy model and find that the effects of noise alone can cause biases of order 1-10% on measured shears, which is significant for current and future lensing surveys. We evaluate a simulation-based calibration method to create a bias model as a function of galaxy properties and observing conditions. This model is then used to correct the simulated measurements. We demonstrate that this method can effectively reduce noise bias so that shear measurement reaches the level of accuracy required for estimating cosmic shear in upcoming lensing surveys., Comment: 12 pages, 4 figures, submitted to MNRAS