The non-zero mass of neutrinos suppresses the growth of cosmic structure on small scales. Since the level of suppression depends on the sum of the masses of the three active neutrino species, the evolution of large-scale structure is a promising tool to constrain the total mass of neutrinos and possibly shed light on the mass hierarchy. In this work, we investigate these effects via a large suite of N -body simulations that include massive neutrinos using an analytic linear-response approximation: the Cosmological Massive Neutrino Simulations (MassiveNuS). The simulations include the effects of radiation on the background expansion, as well as the clustering of neutrinos in response to the nonlinear dark matter evolution. We allow three cosmological parameters to vary: the neutrino mass sum M ν in the range of 0-0.6 eV, the total matter density Ω m , and the primordial power spectrum amplitude A s . The rms density fluctuation in spheres of 8 comoving Mpc/h (σ 8 ) is a derived parameter as a result. Our data products include N -body snapshots, halo catalogues, merger trees, raytraced galaxy lensing convergence maps for four source redshift planes between z s =1-2.5, and ray-traced cosmic microwave background lensing convergence maps. We describe the simulation procedures and code validation in this paper. The data are publicly available at

Weak lensing maps contain information beyond two-point statistics on small scales. Much recent work has tried to extract this information through a range of different observables or via nonlinear transformations of the lensing field. Here we train and apply a 2D convolutional neural network to simulated noiseless lensing maps covering 96 different cosmological models over a range of {Ωm, σ8}. Using the area of the confidence contour in the {Ωm, σ8} plane as a figure-of-merit, derived from simulated convergence maps smoothed on a scale of 1.0 arcmin, we show that the neural network yields ≈ 5× tighter constraints than the power spectrum, and ≈ 4× tighter than the lensing peaks. Such gains illustrate the extent to which weak lensing data encode cosmological information not accessible to the power spectrum or even other, non-Gaussian statistics such as lensing peaks.

Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

Massive cosmic neutrinos change the structure formation history by suppressing perturbations on small scales. Weak lensing data from galaxy surveys probe the structure evolution and thereby can be used to constrain the total mass of the three active neutrinos. However, much of the information is at small scales where the dynamics are nonlinear. Traditional approaches with second order statistics thus fail to fully extract the information in the lensing field. In this paper, we study constraints on the neutrino mass sum using lensing peak counts, a statistic which captures non-Gaussian information beyond the second order. We use the ray-traced weak lensing mocks from the Cosmological Massive Neutrino Simulations (MassiveNuS), and apply LSST-like noise. We discuss the effects of redshift tomography, multipole cutoff max for the power spectrum, smoothing scale for the peak counts, and constraints from peaks of different heights. We find that combining peak counts with the traditional lensing power spectrum can improve the constraint on neutrino mass sum, Ωm, and As by 39%, 32%, and 60%, respectively, over that from the power spectrum alone.

We train neural networks to perform likelihood-free inference from (25 h −1 Mpc) 2 2D maps containing the total mass surface density from thousands of hydrodynamic simulations of the CAMELS project. We show that the networks can extract information beyond one-point functions and power spectra from all resolved scales ( 100 h −1 kpc) while performing a robust marginalization over baryonic physics at the field level: the model can infer the value of Ωm(±4%) and σ8(±2.5%) from simulations completely different to the ones used to train it.

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, and the sensitivity is redshift dependent and is non-Gaussian. We find that redshift tomography significantly improves the constraints on neutrino mass for MFs, compared to the improvements for the 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 [M ν , Ω m , A s ] from the power spectrum, MFs, and their combination. We show that 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 and galaxy shape and redshift biases will be important to realize the full potential of MFs.

We present the Cosmology and Astrophysics with Machine Learning Simulations (CAMELS) Multifield Data set (CMD), a collection of hundreds of thousands of 2D maps and 3D grids containing many different properties of cosmic gas, dark matter, and stars from more than 2000 distinct simulated universes at several cosmic times. The 2D maps and 3D grids represent cosmic regions that span ∼100 million light-years and have been generated from thousands of state-of-the-art hydrodynamic and gravity-only N-body simulations from the CAMELS project. Designed to train machine-learning models, CMD is the largest data set of its kind containing more than 70 TB of data. In this paper we describe CMD in detail and outline a few of its applications. We focus our attention on one such task, parameter inference, formulating the problems we face as a challenge to the community. We release all data and provide further technical details at https://camels-multifield-dataset.readthedocs.io.

We have investigated a recently proposed halo-based model, Camelus, for predicting weak-lensing peak counts, and compared its results over a collection of 162 cosmologies with those from N-body simulations. While counts from both models agree for peaks with S/N > 1 (where S/N is the ratio of the peak height to the r.m.s. shape noise), we find ≈ 50% fewer counts for peaks near S/N = 0 and significantly higher counts in the negative S/N tail. Adding shape noise reduces the differences to within 20% for all cosmologies. We also found larger covariances that are more sensitive to cosmological parameters. As a result, credibility regions in the {Ωm, σ8} are ≈ 30% larger. Even though the credible contours are commensurate, each model draws its predictive power from different types of peaks. Low peaks, especially those with 2 < S/N < 3, convey important cosmological information in N-body data, as shown in [1, 2], but Camelus constrains cosmology almost exclusively from high significance peaks (S/N > 3). Our results confirm the importance of using a cosmology-dependent covariance with at least a 14% improvement in parameter constraints. We identified the covariance estimation as the main driver behind differences in inference, and suggest possible ways to make Camelus even more useful as a highly accurate peak count emulator.