We forecast and optimize the cosmological power of various weak-lensing aperture mass ($M_{\rm ap}$) map statistics for future cosmic shear surveys, including peaks, voids, and the full distribution of pixels (1D $M_{\rm ap}$). These alternative methods probe the non-Gaussian regime of the matter distribution, adding complementary cosmological information to the classical two-point estimators. Based on the SLICS and cosmo-SLICS $N$-body simulations, we build Euclid-like mocks to explore the $S_8 - \Omega_{\rm m} - w_0$ parameter space. We develop a new tomographic formalism which exploits the cross-information between redshift slices (cross-$M_{\rm ap}$) in addition to the information from individual slices (auto-$M_{\rm ap}$) probed in the standard approach. Our auto-$M_{\rm ap}$ forecast precision is in good agreement with the recent literature on weak-lensing peak statistics, and is improved by $\sim 50$% when including cross-$M_{\rm ap}$. It is further boosted by the use of 1D $M_{\rm ap}$ that outperforms all other estimators, including the shear two-point correlation function ($\gamma$-2PCF). When considering all tomographic terms, our uncertainty range on the structure growth parameter $S_8$ is enhanced by $\sim 45$% (almost twice better) when combining 1D $M_{\rm ap}$ and the $\gamma$-2PCF compared to the $\gamma$-2PCF alone. We additionally measure the first combined forecasts on the dark energy equation of state $w_0$, finding a factor of three reduction of the statistical error compared to the $\gamma$-2PCF alone. This demonstrates that the complementary cosmological information explored by non-Gaussian $M_{\rm ap}$ map statistics not only offers the potential to improve the constraints on the recent $\sigma_8$ - $\Omega_{\rm m}$ tension, but also constitutes an avenue to understand the accelerated expansion of our Universe.

/pdf/probing-dark-energy-with-tomographic-weak-lensing-aperture-4ei95ucvjw.pdf

Probing dark energy with tomographic weak-lensing aperture mass statistics

Recent cosmic shear studies have shown that higher-order statistics (HOS) developed by independent teams now outperform standard two-point estimators in terms of statistical precision thanks to their sensitivity to the non-Gaussian features of large-scale structure. The aim of the Higher-Order Weak Lensing Statistics (HOWLS) project is to assess, compare, and combine the constraining power of ten different HOS on a common set of $Euclid$-like mocks, derived from N-body simulations. In this first paper of the HOWLS series, we computed the nontomographic ($\Omega_{\rm m}$, $\sigma_8$) Fisher information for the one-point probability distribution function, peak counts, Minkowski functionals, Betti numbers, persistent homology Betti numbers and heatmap, and scattering transform coefficients, and we compare them to the shear and convergence two-point correlation functions in the absence of any systematic bias. We also include forecasts for three implementations of higher-order moments, but these cannot be robustly interpreted as the Gaussian likelihood assumption breaks down for these statistics. Taken individually, we find that each HOS outperforms the two-point statistics by a factor of around two in the precision of the forecasts with some variations across statistics and cosmological parameters. When combining all the HOS, this increases to a $4.5$ times improvement, highlighting the immense potential of HOS for cosmic shear cosmological analyses with $Euclid$. The data used in this analysis are publicly released with the paper.

Euclid preparation. XXIX. Forecasts for ten different higher-order weak lensing statistics

/pdf/probing-dark-energy-with-tomographic-weak-lensing-aperture-2nlqhtzlxp.pdf

We present KaRMMa, a novel method for performing mass map reconstruction from weak-lensing surveys. We employ a fully Bayesian approach with a physically motivated lognormal prior to sample from the posterior distribution of convergence maps. We test KaRMMa on a suite of dark matter N-body simulations with simulated DES Y1-like shear observations. We show that KaRMMa outperforms the basic Kaiser-Squires mass map reconstruction in two key ways: 1) our best map point estimate has lower residuals compared to Kaiser-Squires; and 2) unlike the Kaiser-Squires reconstruction, the posterior distribution of KaRMMa maps are nearly unbiased in all summary statistics we considered, namely: one-point and two-point functions, and peak/void counts. In particular, KaRMMa successfully captures the non-Gaussian nature of the distribution of $\kappa$ values in the simulated maps. We further demonstrate that the KaRMMa posteriors correctly characterize the uncertainty in all summary statistics we considered. 

OUP accepted manuscript

In this work, which is the first of a series to prepare a cosmological parameter analysis with third-order cosmic shear statistics, we model both the shear three-point correlation functions $\Gamma^{(i)}$ and the third-order aperture statistics $\langle\mathcal{M}_\mathrm{ap}^3\rangle$ from the BiHalofit bispectrum model and validate these statistics with a series of N-body simulations. We then investigate how to bin the shear three-point correlation functions to achieve an unbiased estimate for third-order aperture statistics in real data. Finally, we perform a cosmological parameter analysis on KiDS1000-like mock data with second- and third-order statistics. We recover all cosmological parameters with very little bias. Furthermore, we find that a joint analysis almost doubles the constraining power on $S_8$ and increases the figure-of-merit in the $\Omega_\mathrm{m}$-$\sigma_8$ plane by a factor of 5.9 with respect to an analysis with only second-order shear statistics. Our modelling pipeline is publicly available at https://github.com/sheydenreich/threepoint/releases/.

/pdf/a-roadmap-to-cosmological-parameter-analysis-with-third-3cfwjyg8.pdf

A roadmap to cosmological parameter analysis with third-order shear statistics. I. Modelling and validation

Weak lensing, which is the deflection of light by matter along the line of sight, has proven to be an efficient method for constraining models of structure formation and reveal the nature of dark energy. So far, most weak-lensing studies have focused on the shear field that can be measured directly from the ellipticity of background galaxies. However, within the context of forthcoming full-sky weak-lensing surveys such as Euclid, convergence maps (mass maps) offer an important advantage over shear fields in terms of cosmological exploitation. While it carry the same information, the lensing signal is more compressed in the convergence maps than in the shear field. This simplifies otherwise computationally expensive analyses, for instance, non-Gaussianity studies. However, the inversion of the non-local shear field requires accurate control of systematic effects caused by holes in the data field, field borders, shape noise, and the fact that the shear is not a direct observable (reduced shear). We present the two mass-inversion methods that are included in the official Euclid data-processing pipeline: the standard Kaiser & Squires method (KS), and a new mass-inversion method (KS+) that aims to reduce the information loss during the mass inversion. This new method is based on the KS method and includes corrections for mass-mapping systematic effects. The results of the KS+ method are compared to the original implementation of the KS method in its simplest form, using the Euclid Flagship mock galaxy catalogue. In particular, we estimate the quality of the reconstruction by comparing the two-point correlation functions and third- and fourth-order moments obtained from shear and convergence maps, and we analyse each systematic effect independently and simultaneously. We show that the KS+ method substantially reduces the errors on the two-point correlation function and moments compared to the KS method. In particular, we show that the errors introduced by the mass inversion on the two-point correlation of the convergence maps are reduced by a factor of about 5, while the errors on the third- and fourth-order moments are reduced by factors of about 2 and 10, respectively.

/pdf/euclid-reconstruction-of-weak-lensing-mass-maps-for-non-8ukcwjdeyy.pdf

Euclid: Reconstruction of weak-lensing mass maps for non-Gaussianity studies

Weak lensing, which is the deflection of light by matter along the line of sight, has proven to be an efficient method for constraining models of structure formation and reveal the nature of dark energy. So far, most weak-lensing studies have focused on the shear field that can be measured directly from the ellipticity of background galaxies. However, within the context of forthcoming full-sky weak-lensing surveys such as Euclid, convergence maps (mass maps) offer an important advantage over shear fields in terms of cosmological exploitation. While it carry the same information, the lensing signal is more compressed in the convergence maps than in the shear field. This simplifies otherwise computationally expensive analyses, for instance, non-Gaussianity studies. However, the inversion of the non-local shear field requires accurate control of systematic effects caused by holes in the data field, field borders, shape noise, and the fact that the shear is not a direct observable (reduced shear). We present the two mass-inversion methods that are included in the official Euclid data-processing pipeline: the standard Kaiser & Squires method (KS), and a new mass-inversion method (KS+) that aims to reduce the information loss during the mass inversion. This new method is based on the KS method and includes corrections for mass-mapping systematic effects. The results of the KS+ method are compared to the original implementation of the KS method in its simplest form, using the Euclid Flagship mock galaxy catalogue. In particular, we estimate the quality of the reconstruction by comparing the two-point correlation functions and third- and fourth- order moments obtained from shear and convergence maps, and we analyse each systematic effect independently and simultaneously...

/pdf/euclid-reconstruction-of-weak-lensing-mass-maps-for-non-ahr22fj49k.pdf

Euclid: Reconstruction of Weak Lensing mass maps for non-Gaussianity studies

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Euclid: Reconstruction of weak-lensing mass maps for non-Gaussianity studies

Euclid: Reconstruction of Weak Lensing mass maps for non-Gaussianity studies