Statistics of rare objects and the Integrated Sachs-Wolfe effect in ?CDM N-body simulations

In this thesis we make predictions of extreme elements of large-scale structure (LSS) in the universe. We base our study on the concordance cosmological model, the Lambda Cold-Dark-Matter (?CDM) model, and in doing so we utilise a suite of very large N-body,dark-matter-only simulations. To understand LSS throughout cosmic history, it is vital to quantify the evolution ofthe numbers of objects in the universe. To this end, we perform a numerical investigation into the abundance of dark matter haloes across an unprecedented combination of redshifts and masses. For the very young universe (z > 6), a fit is presented for the numbers of rare haloes that hosted the energetic objects that drove reionization. At lower redshifts we predict number counts of galaxy groups and clusters, the observation of which forms perhaps our current, best method of interpreting nature on large scales. Our low redshift results are based on simulations with very large volumes, which allows us to probe rare objects in a ?CDM universe, including massive clusters, voids and extreme-velocity mergers. These objects challenge our understanding of the universe by exhibiting the extremes of the ?CDM model. With the possible exception of the Bullet Cluster, our simulation results are in line with current observations. We study the late-time Integrated Sachs-Wolfe (ISW) effect using a (6 h-1Gpc)³ volume simulation which contains enough particles (6000³) to resolve luminous red galaxies. From these data we calculate the expected ISW-LSS cross-correlation signal in a ?CDM universe. The signal is found to be strongest for LSS surveys that can probe redshift ranges of z ~ 0.2 to 0.8. The ISW effect promises to be an important measure of the evolution of dark energy, the overall understanding of which is perhaps the most important current goal in cosmology.