Cosmological dynamics and structure formation

Observational surveys which probe our universe deeper and deeper into the nonlinear regime of structure formation are becoming increasing accurate. This makes numerical simulations an essential tool for theory to be able to predict phenomena at comparable scales. In the first part of this thesis we study the behaviour of cosmological models involving a scalar field. We are particularly interested in the existence of fixed points of the dynamical system and the behaviour of the system in their vicinity. Upon addition of spatial curvature to the single-scalar field model with an exponential potential, canonical kinetic term, and a matter fluid, we demonstrate the existence of two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the equation-of-state parameter. In the second part, we numerically simulate collisionless particles in the weak field approximation to General Relativity, with large gradients of the fields and relativistic velocities allowed. To reduce the complexity of the problem and enable high resolution simulations, we consider the spherically symmetric case. Comparing numerical solutions to the exact Schwarzschild and Lemaître-Tolman-Bondi solutions, we show that the scheme we use is more accurate than a Newtonian scheme, correctly reproducing the leading-order post-Newtonian behaviour. Furthermore, by introducing angular momentum, configurations corresponding to bound objects are found. In the final part, we simulate the conditions under which one would expect to form ultracompact minihalos, dark matter halos with a steep power-law profile. We show that an isolated object exhibits the profile predicted analytically. Embedding this halo in a perturbed environment we show that its profile becomes progressively more similar to the Navarro-Frenk-White profile with increasing amplitude of perturbations. Next, we boost the power spectrum at a very early redshift during radiation domination on a chosen scale and simulate clustering of dark matter particles at this scale until low redshift. In this scenario halos form earlier, have higher central densities, and are more compact.