The term *gravitational lensing* describes the fact that the gravitational fields of massive objects (like galaxies and clusters of galaxies) bend the paths of photons as they propagate through the universe. On extra-galactic scales, even the filamentary structure of the cosmic web acts as a gravitational lens. A consequence is that the observed images of distant (i.e. high-redshift) galaxies are distorted from their original shapes. Except in rare cases where the lensing is strong enough to produce elongated arcs and/or multiple images, such distortions are very slight and cannot be detected on individual galaxies. Only by averaging over a large number of galaxies can we detect a statistical signal--this is the regime of *weak lensing*. Weak-lensing analyses will play a key role in achieving the science goals of upcoming galaxy surveys like CFIS and Euclid.

Mass Mapping | Non-Gaussian Structures | Cosmological Parameters |

A successful weak-lensing pipeline depends crucially on accurate measurements of galaxy shapes. Our lab is involved in developing techniques to correct for instrumental effects like the point spread function (PSF) in order to produce high-quality lensing catalogues.

## Mass mapping

Weak lensing allows us to map the structure of the universe, both the dark matter that comprises the cosmic web as well as the luminous matter that traces it. Using catalogs of galaxy positions, redshifts, and their lensed shapes (ellipticities), we can generate maps of the mass distribution that caused the observed lensing. A significant challenge for mass mapping is the problem of missing data. Bright foreground stars, cosmic ray trails, CCD defects, and other spurious (i.e., non-cosmological) signals must be masked out, leaving gaps in the spatial data field. In CosmoStat, we have developed advanced statistical and image processing techniques to cope with missing data and other important problems that arise in weak lensing analyses. In this spirit, our group has developed a robust methodology, based on Bayesian statistics, analytic physical theory and machine learning to address such inverse problems.

The statistics of mass maps provide a way to test alternatives to general relativity (i.e. modified gravity theories) in order to better understand the nature of gravitation. In this vein, our group has worked on distinguishing standard and modified gravity cosmological models using higher-order statistics of mass maps as well as machine learning.

#### Glimpse

Glimpse is a mass-mapping technique developed in our lab that uses a sparsity-based regularisation scheme to recover high-resolution convergence maps. The method has been tested on realistic simulations of galaxy clusters and has also been applied to real data in both small- and large-field contexts. For example, Glimpse was used to reconstruct the mass distribution in the Abell 520 merging galaxy cluster system using Hubble Space Telescope observations. A mass map of the Dark Energy Survey (DES) Science Verification field has also been produced using Glimpse.

The Glimpse source code is freely and publicly available.

## Non-Gaussian structures

On small scales, the structures of the cosmic web are non-Gaussian. This information is therefore not captured by traditional second-order statistics such as the weak-lensing two-point correlation function or power spectrum. *Peaks* in weak-lensing maps, defined as local maxima of the lensing convergence, are tracers of over-dense regions and provide a means to extract higher-order, non-Gaussian information. Our group devised a new model to predict weak-lensing peaks as a function of cosmological parameters. The code is called Camelus and has been studied in a number of publications (1, 2, 3, 4). More recently, our group has developed the "starlet ℓ1-norm" which is another summary statistic designed to capture non-Gaussian cosmological information from weak lensing maps. It is calculated by summing the absolute values of the coefficients obtained from the starlet (or wavelet) decomposition of these maps. It has been shown that it overperforms power spectrum and peak and void statistics combined. Our group is also involved in developing a theoretical prediction for some of these higher-order statistics.

## Cosmological Parameters

Weak lensing is a powerful tool to constrain the model of our universe, its expansion history, and the evolution of the cosmic web. Lensing allows us to measure model parameters such as the total matter density and the "clumpiness" of the cosmic web. This probe also is very promising to test theories beyond the standard model of cosmology, to measure properties of dark energy, and to constrain the laws of gravity on very large scales. CosmoStat scientists have contributed to the cosmological analysis of many large wide-field optical surveys, including CFHTLS, COSMOS, CFHTLenS, and DES. We are strongly involved in upcoming galaxy surveys such as CFIS and Euclid.