Axions, Strings, and Dark-Matter Cosmology

The existence of dark matter is one of the unsolved fundamental problems of physics and cannot be explained by established theories such as general relativity or the standard model of particle physics. However, an extension of Quantum Chromodynamics (QCD), a part of the Standard Model, can explain dark matter. It is known that QCD is invariant under charge and parity symmetry (CP symmetry), the violation of symmetry is quantified by the parameter theta. The invariance of the QCD under CP transformations is not explicitly required, but only implicitly fulfilled by a very small theta parameter. This seemingly arbitrary conservation of CP symmetry is known as the strong CP problem. A promising solution to this problem was presented by Peccei and Quinn, who consider the $\theta$ parameter not as a constant, but as a dynamical field. This requires a new particle that is extremely light and hardly interacts with the matter we know, as it is expected for dark matter. Therefore, this new particle, called axion, potentially solves two problems; the strong CP problem and the origin of dark matter. To date, however, it was not possible to detect this hypothetical particle experimentally, which is, if the particle exist, because of its very weak interaction and therefore very complex experimental set-ups are required for a successful measurement. In addition, there are only a few precise theoretical predictions for the mass of the axion. In this thesis we present a new method to determine the axion mass. This method is able to correctly describe the responsible production mechanisms for the first time and thus predict a precise value of the axion mass by lattice simulations. The challenge lies in the correct description of the production mechanisms, more precisely in the simulation of the correct string tension. Moreover we also present new methods for the microscopic investigation of the string dynamics themselves, with which theoretical equations of motion can be simulated and compared for the first time. This also provides information about the reliability of string simulations in general