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Impressive observational progress over the last decades has led to the establishment of the ΛCDM cosmological model. The ΛCDM model is based on the general theory of relativity and primordial perturbations, and it further relies on two phenomenolog- ically motivated constituents of the Universe, namely dark matter and dark energy. Notwithstanding the success of the ΛCDM model, the nature of these mysterious dark components remains unknown, and their scientific investigation represents one of the greatest challenges of modern cosmology. Current and future surveys provide a wealth of high-precision data by observing dif- ferent properties of the Universe. These cosmological probes are statistically not independent and provide complementary information when their auto- and cross- correlations are considered in the analysis. This requires a corresponding level of precision for the theoretical predictions and estimations of the uncertainties on the observables. Neglecting non-linear and non-Gaussian effects on the latter can bias the results or lead to an under-estimation of the statistical errors on the cosmological pa- rameters. In this thesis, we present UFALCON, a framework to generate correlated full- sky maps for different cosmological probes. The pipeline works by post-processing numerical N -Body simulations, and can be used for the estimation of multi-probe covariance matrices which fully include the non-linearities and non-Gaussianities simulated by the former. We first describe the UFALCON framework and its methodology to generate full-sky maps for weak lensing and galaxy overdensity. We perform a cosmic shear forecast analysis using a UFALCON-based covariance matrix, and assess its accuracy of using the comoving Lagrangian acceleration method to simulate the underlying matter field. Subsequently, we extend the framework by adding the functionality to generate a set of correlated full-sky maps for weak lensing shear, CMB lensing convergence, galaxy overdensity, and CMB temperature anisotropies from the integrated Sachs-Wolfe i effect. We then perform a forecast analysis to investigate the effect of combining dif- ferent cosmological probes and using a UFALCON-based covariance matrix compared to using a Gaussian approximation. A significant increase in constraining power is observed when cross-correlations are included in the analysis. Furthermore, using a non-Gaussian covariance matrix becomes increasingly important as more probes and cross-correlations are considered. Using a UFALCON-based multi-probe covariance matrix, we then perform a combined analysis of 46 auto- and cross-spherical harmonic power spectra using CMB tempera- ture and polarisation anisotropies and CMB lensing from PLANCK, galaxy clustering from the Baryon Oscillation Spectroscopic Survey, and weak lensing shear from the Kilo-Degree Survey. By additionally varying probe-specific nuisance parameters as well as the sum of the masses of neutrinos, we obtain consistent and competitive parameter constraints. Finally, we highlight further applications of the weak lensing part of UFALCON. These include the covariance matrix estimation for the cosmic shear analysis of the Dark Energy Survey Year 1 data based on Monte-Carlo Control Loops, the usage of UFALCON weak lensing maps for a forecast analysis based on non-Gaussian statistics and as training data for convolutional neural networks. Overall, the UFALCON framework provides a fast and accurate pipeline to generate correlated non-Gaussian maps for various cosmological probes, suitable for integrated analyses of current and future survey data. |
