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.