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We present a cosmological analysis using the second and third moments of the weak lensing mass (convergence) maps from the first three years of data (Y3) data of the Dark Energy Survey (DES). The survey spans an effective area of 4139 square degrees and uses the images of over 100 million galaxies to reconstruct the convergence field. The second moment of the convergence as a function of smoothing scale contains information similar to standard shear 2-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The data is analysed in the context of the $\Lambda$CDM model, varying 5 cosmological parameters and 19 nuisance parameters modelling astrophysical and measurement systematics. Our modelling of the observables is completely analytical, and has been tested with simulations in our previous methodology study. We obtain a 1.7\% measurement of the amplitude of fluctuations parameter $S_8\equiv \sigma_8 (\Omega_m/0.3)^{0.5} = 0.784\pm 0.013$. The measurements are shown to be internally consistent across redshift bins, angular scales, and between second and third moments. In particular, the measured third moment is consistent with the expectation of gravitational clustering under the $\Lambda$CDM model. The addition of the third moment improves the constraints on $S_8$ and $\Omega_{\rm m}$ by $\sim$15\% and $\sim$25\% compared to an analysis that only uses second moments. We compare our results with {\it Planck} constraints from the Cosmic Microwave Background (CMB), finding a $2.2$ \textendash $2.8\sigma$ tension in the full parameter space, depending on the combination of moments considered. The third moment independently is in $2.8\sigma$ tension with {\it Planck}, and thus provides a cross-check on analyses of 2-point correlations., Comment: 27 pages, 20 figures, accepted for publication in PRD

We constrain the matter density $\Omega_{\mathrm{m}}$ and the amplitude of density fluctuations $\sigma_8$ within the $\Lambda$CDM cosmological model with shear peak statistics and angular convergence power spectra using mass maps constructed from the first three years of data of the Dark Energy Survey (DES Y3). We use tomographic shear peak statistics, including cross-peaks: peak counts calculated on maps created by taking a harmonic space product of the convergence of two tomographic redshift bins. Our analysis follows a forward-modelling scheme to create a likelihood of these statistics using N-body simulations, using a Gaussian process emulator. We include the following lensing systematics: multiplicative shear bias, photometric redshift uncertainty, and galaxy intrinsic alignment. Stringent scale cuts are applied to avoid biases from unmodelled baryonic physics. We find that the additional non-Gaussian information leads to a tightening of the constraints on the structure growth parameter yielding $S_8~\equiv~\sigma_8\sqrt{\Omega_{\mathrm{m}}/0.3}~=~0.797_{-0.013}^{+0.015}$ (68% confidence limits), with a precision of 1.8%, an improvement of ~38% compared to the angular power spectra only case. The results obtained with the angular power spectra and peak counts are found to be in agreement with each other and no significant difference in $S_8$ is recorded. We find a mild tension of $1.5 \thinspace \sigma$ between our study and the results from Planck 2018, with our analysis yielding a lower $S_8$. Furthermore, we observe that the combination of angular power spectra and tomographic peak counts breaks the degeneracy between galaxy intrinsic alignment $A_{\mathrm{IA}}$ and $S_8$, improving cosmological constraints. We run a suite of tests concluding that our results are robust and consistent with the results from other studies using DES Y3 data.

We present cosmological constraints for the flat $\Lambda$CDM model, including the sum of neutrino masses, by performing a multi-probe analysis of a total of 13 tomographic auto- and cross-angular power spectra. This is achieved by combining, at map level, the latest primary CMB and CMB-lensing measurements from the Planck 2018 data release, as well as spectroscopic galaxy samples from BOSS DR12, and the latest Kilo-Degree Survey (KiDS-1000) tomographic weak lensing shear data release. Our analysis includes auto- and cross-correlations as well as calibration parameters for all cosmological probes, thus providing a self-calibration of the combined data sets. We find a good fit (reduced $\chi^2$=1.7) for the combined probes with calibration parameters only moderately different from their nominal value, thus giving a possible interpretation of the tension between the early- and late-Universe probes. The resulting value for the structure growth parameter is $S_8 = 0.754 \pm 0.016$ (68\% CL). We also obtain a $\sim$2.3$\sigma$ constraint on the neutrino mass sum of $\sum m_\nu = 0.51^{+0.21}_{-0.24}$ eV (68\% CL), which is compatible with current particle physics limits. We perform several tests by fixing the neutrino mass sum to a low value, considering narrower priors on the multiplicative bias parameters for cosmic shear, and by fixing all calibration parameters to their expected values. These tests result in worse fits compared to our fiducial run, especially for the case when all calibration parameters are fixed. This latter test also yields a lower upper limit of the neutrino mass sum. We discuss how the interplay between the cosmological and calibration parameters impact the $S_8$-tension and the constraints on the neutrino mass sum. [abridged], Comment: 40 pages

Assume that $\Omega\subset \mathbb{R}^k$ is an open set, $V$ is a separable Banach space over a field $\mathbb K\in\{\mathbb R,\mathbb C\}$ and $f_1,\ldots,f_N \colon\Omega\to \Omega$, $g_1,\ldots, g_N\colon\Omega\to \mathbb{K}$, $h_0\colon \Omega\to V$ are given functions. We are interested in the existence and uniqueness of solutions $\varphi\colon \Omega\to V$ of the linear functional equation $\varphi=\sum_{k=1}^{N}g_k\cdot(\varphi\circ f_k)+h_0$ in Lorentz spaces.

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.

We study betweenness preserving mappings (we call them \emph{monotone}) defined on subsets of the plane. Once the domain is a convex set, such a mapping is either the restriction of a homography, or its image is contained in the union of a line and a single point, or its image consists of five points, one of them being between two disjoint pairs of the other four points. We also show that an open planar set cannot be mapped in a one-to-one monotone way into the real line. From this we deduce that a one-to-one monotone mapping from a convex planar set with nonempty interior is necessarily a partial homography. Finally, we prove that a set consisting of three pairwise non-parallel lines does not admit a one-to-one monotone mapping into the real line, while on the other hand a set consisting of three closed line segments intersecting at a single point does admit such a mapping., Comment: Final version (21 pages, 4 figures)

For the next generation of spectroscopic galaxy surveys, it is important to forecast their performances and to accurately interpret their large data sets. For this purpose, it is necessary to consistently simulate different populations of galaxies, in particular Emission Line Galaxies (ELGs), less used in the past for cosmological purposes. In this work, we further the forward modeling approach presented in Fagioli et al. 2018, by extending the spectra simulator Uspec to model galaxies of different kinds with improved parameters from Tortorelli et al. 2020. Furthermore, we improve the modeling of the selection function by using the image simulator Ufig. We apply this to the Sloan Digital Sky Survey (SDSS), and simulate $\sim157,000$ multi-band images. We pre-process and analyse them to apply cuts for target selection, and finally simulate SDSS/BOSS DR14 galaxy spectra. We compute photometric, astrometric and spectroscopic properties for red and blue, real and simulated galaxies, finding very good agreement. We compare the statistical properties of the samples by decomposing them with Principal Component Analysis (PCA). We find very good agreement for red galaxies and a good, but less pronounced one, for blue galaxies, as expected given the known difficulty of simulating those. Finally, we derive stellar population properties, mass-to-light ratios, ages and metallicities, for all samples, finding again very good agreement. This shows how this method can be used not only to forecast cosmology surveys, but it is also able to provide insights into studies of galaxy formation and evolution., Comment: 28 pages, 10 figures, accepted for publication in JCAP