| Observations of the large-scale structure of the universe provide important tests of cosmology. I explore two ways how such observations can be compared with cosmological models, and look at some of the theoretical questions underlying the formation of large-scale structure.; The first approach uses the evolution of the number density of galaxy clusters with time, which strongly depends on the density and other parameters of the universe. The optimum observation strategy for X-ray telescopes (Chandra and XMM) is determined which yields the largest number of clusters at high redshifts. The cluster numbers are large enough to differentiate between various inflation-based cosmological scenarios if redshifts are established by follow-up observations. Since these predictions are based on cosmological simulations, I compare different ways how clusters are identified in simulations and which one gives the most reliable results.; The second approach looks at the geometry of large-scale structure in redshift surveys. I use a statistic which quantifies its degree of linearity, planarity, and sphericity. The presence of linear (fingers of God) and planar (the Great Wall) structures is detected in the CfA2 survey. There are no systematic differences between mock surveys constructed from simulations and the CfA2 survey. Different realizations of mock surveys from the same simulation show variations which are larger than the differences between the cosmological models. It appears that the CfA2 survey has not reached the scale of homogeneity.; At a more theoretical level is the question when the different structures emerged from the initial density perturbations. In the cosmic web hypothesis, spherical structures appear first with filaments growing between them, followed by walls connecting the filaments. By using the structure functions to trace the evolution of the geometry of large-scale structure in simulations, I find that this picture is not correct, and that instead filaments and sheets grow simultaneously.; In the theory of the origin and evolution of density perturbations, a criticism of the gauge-invariant approach has been put forward. I point out a mistake in the criticism, and construct a counterexample to its claims. |
