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For many years, observations of the Universe suggest a series problems with our theoretical models, particularly its dark energy and dark matter components. Fortunately, the Universe also provides us with a tool to solve these problems, called strong gravitational lensing. This natural phenomenon, observed as multiple images of a distant background source, distorted by the mass of a foreground galaxy, offers a unique opportunity to detect the otherwise invisible total mass of that galaxy. Yet, this detection is only possible if both background and foreground objects are accurately modeled, a task of increasing difficulty because our telescopes reveal more and more of the intrinsic complexity of galaxies. The primary goal of this thesis is to demonstrate how novel and well-motivated techniques can go beyond the current simplifying assumptions to improve the modeling of luminous and dark components of galaxies. Gravitational lens modeling is an under-constrained problem that has several possible solutions. The new techniques I introduce here are based on two key concepts to overcome this difficulty: sparsity and the wavelet transform. Sparsity selects the solution that contains the fewest parameters, namely the least complex one that best fits the observation. The wavelet transform separates the various spatial scales of the solution and enables the reconstruction of the small-scale compact features up to the larger, smoother variations, which are all found in real galaxies. Since the complexity and size of data sets are dramatically increasing, modeling techniques must also be fast and scalable. I address these requirements using differentiable programming to enable unprecedented gains in computation time. The proposed modeling framework allows us to effortlessly combine simple and more complex techniques together, if required by the observations. In this work, I demonstrate that sparsity and wavelets can address the limitations of current methods for modeling the full complexity of gravitational lenses. Compared to the many methods based on smoothness assumptions, I show how multi-scale modeling techniques significantly improve the reconstruction of lensed galaxies at high resolution. Moreover, I demonstrate that those same techniques are well-suited to characterize the invisible mass distributions of galaxies, notably when it deviates from the widely used smooth elliptical profiles. These results offer exciting possibilities to measure better the properties of galaxies via gravitational lensing, including their dark matter content, ultimately improving our understanding of galaxy evolution. Additionally, I take part to the long-standing debate regarding the role of dark energy in the expansion of the Universe using the method of time-delay cosmography. Based on the gravitational lensing of distant quasars, this method plays a central role in this context because it can measure the expansion rate of the Universe (the Hubble constant) independently of all other methods. The results I present are various: searching for systematic errors in past measurements, testing modeling techniques on a blind challenge, and modeling recent Hubble Space Telescope observations of lensed quasars to measure their absolute distance. I also describe the new approach introduced within the TDCOSMO collaboration, based on relaxing most assumptions on the mass distribution of galaxies and replacing those with observations of stellar kinematics.

Analyzing gravitationally lensed objects enables a wide range of physical and cosmological applications, such as probing the dark matter content in galaxies and clusters or measuring the Universe's expansion rate. The precision of these applications can be improved drastically with a larger number of lenses. For this reason, finding new strong gravitational lensing systems is crucial. Traditionally, gravitational lenses were found with meticulous visual inspections of imaging datasets. However, the next generation of large-scale imaging surveys will produce such a large amount of data that visual inspection will be unpractical, thus motivating the development of efficient automated detection methods to handle large datasets and improve the accuracy of the different applications. The main topic of this thesis is to develop and improve our lens finding algorithms and to study new strong gravitational lenses in large-scale imaging surveys. The first part of this thesis has been to develop a new tool that allows the production of lens simulations. Deep learning algorithms, particularly convolutional neural networks (CNNs), have recently proven their efficiency in detecting lensing systems. In particular, CNNs can be adapted to find a large variety of lenses at once, making them especially suited to be part of automated detection pipelines. However, convolutional neural networks usually require large sets of images to be trained. Unfortunately, the number of known lenses is at this time too low to constitute a sufficient training set. For this reason, robust and flexible tools to simulate realistic lenses have to be developed to generate training sets. Lens simulations must, however, be as realistic as possible to avoid biases. In this thesis, we propose a simulation tool that enables the production of large sets of realistic lens simulations. This tool has been designed to be flexible and, thus, enables the production of lens simulations with different types of deflectors for any imaging survey. The second part consists in separating the light of a lensed source from the foreground object. Indeed, in some cases, the lens features are hidden by the light of the foreground object and deblending might help to identify the lenses help identify lenses with small image separation and enables photometric redshift measurements or the initialization of lens models. This thesis presents a new data-driven method for deblending strong gravitational lenses based on neural networks. Finally, due to the low occurrence rate of strong lensing, the false positive rate of detection algorithms is still a significant challenge. Therefore, we present different tools that enable the inspection of large sets of candidate images. In addition, evaluating the quality of lens candidates is somewhat subjective since the features that define a lens may differ for different experts. Therefore, we propose a set of grading guidelines that can be used for the subsequent ground-based imaging lens searches in this thesis. The CNN-based classifier, the deblending algorithm, and the simulation and visualization tools are part of an automated lens-finding pipeline. This flexible pipeline can be adapted to future large-scale surveys. We discuss in this thesis its first applications to the Canada-France Imaging Survey and the Dark Energy Survey, which led to the discovery of 133 and 403 high-quality lens candidates, respectively.

During these last decades, by virtue of observations, the Standard Cosmological Model has emerged, providing a description of the Universe's evolution using a minimal set of independent constraints - the cosmological parameters. Among them is the expansion rate of the Universe, the so-called Hubble constant or H0, first measured by Lemaître in 1927. The century that followed this cornerstone measurement saw numerous attempts to refine the initial value, and for good reason: a precise and independent measurement of H0 will bring strong constraints on the cosmological models. It could notably help the astronomers to better understand the nature of dark energy, thus making it one of the most sought-after prizes in modern cosmology. My work at the Laboratory of Astrophysics of EPFL is embedded in this context. I am part of the COSMOGRAIL and H0LiCOW collaborations, aiming to measure the Hubble constant with the highest level of precision using time-delay cosmography, a method based on the theory of strong gravitational lensing. This effect occurs when an observer looks at a light source located behind a massive foreground galaxy. The mass of the galaxy acts similarly to an optical lens and focuses the light rays emitted by the source. As a consequence, multiple lensed images of the source appear around the lens galaxy. If the luminosity of the source changes over time, the variations will be seen in all the lensed images but with a temporal delay due to the different travel paths of the light rays. By carefully monitoring the luminosity variations of each lensed image, one can precisely measure the temporal delays between them. Combined to high-resolution observations of the foreground galaxy and its surroundings, it is possible to directly measure the Hubble constant upon the sole assumption that the General Relativity is correct. Since more than 13 years, COSMOGRAIL monitors dozens of lensed quasars to produce high-quality light curves and time-delay measurements. During these last four years, I took care of the monitoring schedule, continuous data reduction and time-delay measurements through the development of curve-shifting techniques. I produced light curves and measured time delays on a variety of lenses. After more than a decade of endeavours, COSMOGRAIL and H0LiCOW finally revealed their measurement of the expansion rate of the Universe from a blind analysis of three lensed sources. I had the privilege to be the lead author of the publication presenting our measurement of the Hubble constant, H0=71.9 -3.0+2.4 km/s/Mpc 3.8% precision in the Standard Cosmological Model. Such a precision allows a direct comparison with the results of the distance ladder technique in the local Universe and the Planck satellite Cosmic Microwave Background observations in the distant Universe, both of which being currently in a significant tension of unknown source.