Challenges of theoretical and numerical structure formation in a ΛCDM universe

Systematic surveys of the extra-galactic sky have revealed the existence of large-scale structures in the Universe: the galaxy distribution is organized in a complex network of filaments surrounding underdense regions and crossing at density peaks which host galaxy clusters. These structures are believed to form through gravitational instability starting from quantum density fluctuations in the primordial Universe.Perhaps surprisingly -- considering the huge dynamical range and complexity of the Universe -- recent years have witnessed the emergence of a cosmological concordance model, dubbed ΛCDM. The first two chapters provide a summary of the theoretical background of the components of this model. During the last two decades, numerical simulations have become a powerful tool to study astronomical objects on a large range of scales. They are used extensively in all areas of astronomy and astrophysics: e.g. the formation of single stars and planets, analyzing the dynamics of star clusters, modeling hydrodynamical processes in galaxies like our Milky Way, and last but not least studying the large-scale structure of cosmological volumes. We describe the general methodology of cosmological N-body simulations, its strengths and limitations, and the specific implementation used in this work, the Gadget-2 code. The following chapters rely heavily on results of such simulations, as they can be used to test theoretical predictions or compare the ΛCDM model with observational data. After this technical introduction, we describe a novel numerical method to test perturbative methods for computing the density contrast of dark matter, and compare the result against full N-body simulations. In addition, we test the validity of a popular bias model and find that it lacks the accuracy required to fully exploit the statistical power of upcoming galaxy surveys. The next chapter deals with local primordial non-Gaussianity (PNG), a specific type of initial conditions for structure formation. While the most stringent constraints on primordial non-Gaussianity currently come from the cosmic microvwave background (CMB), galaxy clustering provides an independent validation of these results, and future large-scale structure surveys are even predicted to surpass the CMB constraints. However, we show that galaxy clustering suffers from specific parameter degeneracies which are not present in the CMB. We caution against the commonly used simple model to measure PNG parameters, and instead promote Bayesian model selection to asses the influence of these degeneracies in the data. The final chapter addresses the subject of near-field cosmology, i.e. the concept of supplementing the constraints on the overall cosmological model with small-scale information from the local Universe. In particular, this chapter deals with the dynamical properties of simulated subhalos around high-resolution Milky-Way sized dark matter halos, representative of the population of dwarf galaxies around our own Galaxy. We investigate the physical conditions needed to rapidly circularize the orbits of infalling systems, possibly giving rise to peculiar stellar streams such as the recently observed Monoceros overdensity