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The influx of massive amounts of data from current and upcoming cosmological surveys necessitates compression schemes that can efficiently summarize the data with minimal loss of information. We introduce a method that leverages the paradigm of self-supervised machine learning in a novel manner to construct representative summaries of massive datasets using simulation-based augmentations. Deploying the method on hydrodynamical cosmological simulations, we show that it can deliver highly informative summaries, which can be used for a variety of downstream tasks, including precise and accurate parameter inference. We demonstrate how this paradigm can be used to construct summary representations that are insensitive to prescribed systematic effects, such as the influence of baryonic physics. Our results indicate that self-supervised machine learning techniques offer a promising new approach for compression of cosmological data as well its analysis.

Strong gravitational lensing has emerged as a promising approach for probing dark matter models on sub-galactic scales. Recent work has proposed the subhalo effective density slope as a more reliable observable than the commonly used subhalo mass function. The subhalo effective density slope is a measurement independent of assumptions about the underlying density profile and can be inferred for individual subhalos through traditional sampling methods. To go beyond individual subhalo measurements, we leverage recent advances in machine learning and introduce a neural likelihood-ratio estimator to infer an effective density slope for populations of subhalos. We demonstrate that our method is capable of harnessing the statistical power of multiple subhalos (within and across multiple images) to distinguish between characteristics of different subhalo populations. The computational efficiency warranted by the neural likelihood-ratio estimator over traditional sampling enables statistical studies of dark matter perturbers and is particularly useful as we expect an influx of strong lensing systems from upcoming surveys.

A major question in cosmology is what sourced the curvature perturbations that grew into the large-scale structure of the universe that we observe today. Under the assumption that cosmological perturbations were generated from quantum fluctuations during inflation, features in the Cosmic Microwave Background (CMB) temperature and polarization power spectra constrain features in the inflationary potential. Currently our best constraints on the shape of the primordial power spectrum at large scales come from observations of the CMB anisotropies by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite. Oscillatory features in the CMB temperature power spectrum have been interpreted as possible evidence for new physics during inflation. It has been shown that a model with a sharp step in the inflationary potential can give rise to these oscillations. In the first part of the thesis, we show that upcoming polarization measurements provide fertile ground for consistency checks on inflationary models proposed to explain these features. As predictions of specific models of inflation, polarization statistics move beyond a posteriori inferences. In the second part of the thesis, we propose an accurate prescription to map constraints from the CMB onto constraints on the shape of the inflationary potential in a model independent manner, allowing for order unity deviations in the slow-roll parameters. In this formalism, there is a single source function that is responsible for the observable features and it is simply related to the local slope and curvature of the inflaton potential. In the final part, we use this formalism to test the hypotheses of single-field and slow-roll inflation. This analysis greatly simplifies the testing of inflationary models in that it can be used to constrain parameters of specific models of inflation without requiring a separate likelihood analysis for each choice. Our results show that there is no significant evidence for deviations from slow roll across the entire range of scales observable to WMAP. As a test of single-field inflation, we present predictions for the polarization power spectrum. Single field inflation makes falsifiable predictions for the acoustic peaks in the polarization, whose violation would require extra degrees of freedom.

Through likelihood analyses of both current and future data that constrain both the expansion history of the universe and the clustering of matter fluctuations, we provide falsifiable predictions for three broad classes of models that explain the accelerated expansions of the universe: \\(\\Lambda\\)CDM, the quintessence scenario and a more general class of smooth dark energy models that can cross the phantom barrier \\(w(z)=-1\\). Our predictions are model independent in the sense that we do not rely on a specific parametrization, but we instead use a principal component (PC) basis function constructed a priori from a noise model of supernovae and Cosmic Microwave Background observations. For the supernovae measurements, we consider two type of surveys: the current JLA and the upcoming WFIRST surveys. We show that WFIRST will be able to improve growth predictions in curved models significantly. The remaining degeneracy between spatial curvature and \\(w(z)\\) could be overcome with improved measurements of \\(\\sigma_8 \\Omega_m^{1/2}\\), a combination that controls the amplitude of the growth of structure. We also point out that a PC-based Figure of Merit reveals that the usual two-parameter description of \\(w(z)\\) does not exhaust the information that can be extracted from current data (JLA) or future data (WFIRST).

Many dark matter (DM) models that are consistent with current cosmological data show differences in the predicted (sub)halo mass function, especially at sub-galactic scales, where observations are challenging due to the inefficiency of star formation. Strong gravitational lensing has been shown to be a useful tool for detecting dark low-mass (sub)halos through perturbations in lensing arcs, therefore allowing the testing of different DM scenarios. However, measuring the total mass of a perturber from strong lensing data is challenging. Over or underestimating perturber masses can lead to incorrect inferences about the nature of DM. In this paper, we argue that inferring an effective slope of the dark matter density profile, which is the power-law slope of perturbers at intermediate radii, where we expect the perturber to have the largest observable effect, is a promising way to circumvent these challenges. Using N-body simulations, we show that (sub)halo populations under different DM scenarios differ in their effective density slope distributions. Using realistic mocks of Hubble Space Telescope observations of strong lensing images, we show that the effective density slope of perturbers can be robustly measured with high enough accuracy to discern between different models. We also present our measurement of the effective density slope \\(\\gamma=1.96\\substack{+0.12 \\\ -0.12}\\) for the perturber in JVAS B1938+666, which we find to be a \\(2\\sigma\\) outlier of the cold dark matter scenario. More measurements of this kind are needed to be able to draw robust conclusions about the nature of dark matter.

Upcoming cosmic microwave background (CMB) lensing measurements and tomographic galaxy surveys are expected to provide us with high-precision data sets in the coming years, thus paving the way for fruitful cross-correlation analyses. In this paper we study the information content of the weighted skew-spectrum, a nearly-optimal estimator of the angular bispectrum amplitude, as a means to extract non-Gaussian information on both bias and cosmological parameters from the bispectra of galaxies cross-correlated with CMB lensing, while gaining significantly on speed. Our results show that for the combination of the Planck satellite and the Dark Energy Spectroscopic Instrument (DESI), the difference in the constraints on bias and cosmological parameters from the skew-spectrum and the bispectrum is at most \\(17\\%\\). We further compare and find agreement between our theoretical skew-spectra and those estimated from N-body simulations, for which it is important to include gravitational non-linearities beyond perturbation theory and the post-Born effect for CMB lensing. We define an algorithm to apply the skew-spectrum estimator to the data and, as a preliminary step, we use the skew-spectra to constrain bias parameters and the amplitude of shot noise from the simulations through a Markov chain Monte Carlo likelihood analysis, finding that it may be possible to reach percent-level estimates for the linear bias parameter \\(b_1\\).

Examining the properties of subhalos with strong gravitational lensing images can shed light on the nature of dark matter. From upcoming large-scale surveys, we expect to discover orders of magnitude more strong lens systems that can be used for subhalo studies. To optimally extract information from a large number of strong lensing images, machine learning provides promising avenues for efficient analysis that is unachievable with traditional analysis methods, but application of machine learning techniques to real observations is still limited. We build upon previous work, which uses a neural likelihood-ratio estimator, to constrain the effective density slopes of subhalos and demonstrate the feasibility of this method on real strong lensing observations. To do this, we implement significant improvements to the forward simulation pipeline and undertake careful model evaluation using simulated images. Ultimately, we use our trained model to predict the effective subhalo density slope from combining a set of strong lensing images taken by the \\textit{Hubble Space Telescope}. We found the subhalo slope measurement of this set of observations to be steeper than the slope predictions of cold dark matter subhalos. Our result adds to several previous works that also measured high subhalo slopes in observations. Although a possible explanation for this is that subhalos with steeper slopes are easier to detect due to selection effects and thus contribute to statistical bias, our result nevertheless points to the need for careful analysis of more strong lensing observations from future surveys.