Models of large scale structure formation in cosmology

Combining all knowledge we have gathered about the origin, evolution and current state of the universe it appears indisputable that 95% of the mass-energy density in today's universe is comprised of unknown substances called dark matter and dark energy. This thesis explores different aspects of and develops models for the formation of the largest structures we observe in the universe, because these structures -- the cosmic web made of dark matter halos, clusters of galaxies and galaxies -- sensitively depend on properties of dark matter and dark energy, in particular on their abundances, the equation of state of and possible new interactions mediated by dark energy. Current and upcoming surveys map the large scale structure (LSS) with increasingly higher precision and in larger volumes. In order to optimally extract cosmological parameters we need to build accurate models for LSS formation that also describe how LSS is perceived by real observers trough processes affecting light propagation. Only then can we reliably reconstruct the cosmological parameters and identify the models for dark matter and dark energy preferred by the data. Therefore this thesis contributes to the endeavor to ultimately uncover the nature of dark matter and dark energy. Chapter 2 studies a dark energy model which mediates a ``fifth force'' enhancing Newtonian gravity only on large scales due to the chameleon mechanism, but leads to an expansion history indistinguishable from the case where dark energy is a cosmological constant. Hence the only observables that can discriminate them are related to structure formation. We study the abundance of dark matter halos per halo mass with semi-analytical techniques to find a fit function depending on the model parameter responsible for the range and strength of the fifth force. We find good agreement with Monte-Carlo and N-body simulations of the mass function. Our result is a fit function for the halo mass function that can be used to constrain this model and to look for signatures of the chameleon effect in observations of galaxy of clusters. In Chapters 3 and 4 we show why it is justified to use Newtonian gravity instead of General Relativity on all scales to accurately describe LSS formation in a universe governed by a cosmological constant and cold dark matter. In Chapter 5 we show that a complex scalar field solving the Schrödinger-Poisson equation is able describe collisionless selfgravitating dark matter with the same number of degrees of freedom as the popular dust fluid. In contrast to the dust model it does not suffer from singularities and thus allows the analytical and numerical study of fully nonlinear effects like halo formation. In Chapter 6 we study the clustering of halos as observed in redshift space, by developing an improved model for the halo dynamics based on a coarse grained dust model and by extending the so called Gaussian streaming model to general phase space distribution functions. We compare our results to a N-body simulation halo catalog and find that the coarse grained dust model significantly improves the accuracy of theoretical redshift space correlation functions.