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A bstract We construct and simulate the dynamics of gauged vortons — circular loops of cosmic string supported by the angular momentum of trapped charge and current and provide additional details on the fully stable vorton that we have previously presented. We find that their existence and dynamical properties can be accurately predicted by an analysis based on infinite, straight superconducting strings if an additional constraint on their phase frequency is satisfied. We show a good quantitative agreement with the thin string approximation (TSA) and provide evidence that curvature corrections are inversely proportional to the vorton radius. This is verified with an energy minimisation algorithm that produces vorton solutions and subsequent axial and full three dimensional evolution codes. We find that we can predict the frequencies of each mode of oscillation, determine which modes are unstable and calculate the growth rate of the unstable modes to a high degree of accuracy.

A common prediction of beyond Standard Model theories is the existence of topological solitons that can have significant effects in cosmology. Due to the large range of energy scales at which defects can form, their effects can vary from causing conflict with observations — thus ruling out potential models — to providing answers to some of the most elusive questions in cosmology, such as the dark matter and baryon asymmetry problems. In this thesis, we examine various types of topological defects and compare theoretical predictions to numerical simulations.We begin by constructing and simulating the dynamics of gauged vortons — circular loops of cosmic string supported by the angular momentum of trapped charge and current. We find that their existence and dynamical properties can be accurately predicted by an analysis based on infinite, straight superconducting strings. We also present the strongest evidence to date that it is possible for vortons to be stable to non-axial extrinsic perturbations. The pinching instabilities exhibited by some of our vorton solutions are then examined in more detail, where it is shown that the thin string approximation (TSA) accurately predicts the onset of instability. A stability analysis is developed that is applicable to small wavelength perturbations, where the TSA breaks down.Finally, we discuss the Two Higgs Doublet Model (2HDM) with a particular focus on investigating the effects of gauging the continuous Higgs family accidental symmetries. We find that SO(3)HF symmetric models always suffer from the presence of a single Goldstone boson, but there are a wide range of parameters in the gauged U(1)PQmodel that do not have this problem. It is also possible in this case, under a specific parameter restriction, to recover the bosons of the standard model with one additional massive gauge boson. We discuss the associated gauged topological defects of each scenario and present gauged monopole and string solutions within the 2HDM. The phenomena of localised neutral vacuum condition violation on 2HDM defects is also discussed, with preliminary theoretical ideas and simulations.

We construct and analyse two-dimensional, current-carrying ring solutions, known as kinky vortons, in the \\(Z_2\\)-symmetric global two-Higgs-doublet model (2HDM). We demonstrate the existence of multiple dynamically stable configurations that persist under non-axially symmetric perturbations. These solutions are described with high accuracy by the thin string approximation and elastic string formalism, which correctly capture both their equilibrium radii and dynamical oscillation frequencies. Kinky vortons in the \\(Z_2\\)-symmetric theory establish the viability of vorton solutions in a phenomenologically motivated extension of the Standard Model, and should provide a computationally tractable proxy for vortons in the \\(U(1)\\)-symmetric 2HDM. In addition, we identify a composite domain wall configuration in which localized condensates are supported on secondary domain walls existing on a \\(Z_2\\) wall, suggesting a mechanism by which kinky-vorton-like defects could arise in a three dimensional setting.

We discuss key aspects of the nature of radiation from global strings and its impact on the relic axion density. Using a simple model we demonstrate the dependence on the spectrum of radiation emitted by strings. We then study the radiation emitted by perturbed straight strings paying particular attention to the difference between the overall phase of the field and the small perturbations about the string solution which are the axions. We find that a significant correction is required to be sure that one is analyzing the axions and not the self-field of the string. Typically this requires one to excise a sizeable region around the string - something which is not usually done in the case of numerical field theory simulations of string networks. We have measured the spectrum of radiation from these strings and find that it is compatible with an exponential, as predicted by the Nambu-like Kalb-Ramond action, and in particular is not a ``hard'' spectrum often found in string network simulations. We conclude by attempting to assess the uncertainties on relic density and find that this leads to a range of possible axion masses when compared to the measured density from the Cosmic Microwave Background, albeit that they are typically higher than what is predicted by the Initial Misalignment Mechanism. If the decay is via a ``soft spectrum'' from loops produced close to the backreaction scale we find that \\(m_ a 160\\, eV\\) and a detection frequency \\(f 38\\, GHz\\). If axions are emitted directly by the string network, and we use emission spectra reported in field theory simulations, then \\(m_ a 4\\, eV\\) and \\(f 1\\, GHz\\), however this increases to \\(m_a 125\\, eV\\) and \\(f 30\\, GHz\\) using our spectra for the case of an oscillating string. In all scenarios there are significant remaining uncertainties that we delineate.

We discuss monopoles formed due to the spontaneous breakdown of a global \\(SO(3)_ HF\\) symmetry within the global two-Higgs doublet model. We explain that the Higgs sector dynamics can be described in terms of two vectors one of which is null, \\(R^A=(R^0,R^a,R^4,R^5)\\) for \\(a=1,2,3\\), with 5 independent components describing the Higgs family symmetry and another, \\(n^a\\), with 3 independent components related to the ``would-be'' Goldstone bosons. When formed from random initial conditions we find that monopoles are formed with a charged vacuum in the centre which couples the two fields together. We find a spherical symmetric solution which is an approximately uniform, unit winding of the sphere in both the \\(R^a\\) and \\(n^a\\) vectors. These global monopoles are closely related to the Nambu monopole. The additional complexity and structure contained in these monopoles does not appear to prevent the scaling of their density.

Domain walls formed during a phase transition in a simple field theory model with \\(Z_2\\) symmetry in a periodic box have been demonstrated to annihilate as fast as causality allows and their area density scales \\( t^-1\\). We have performed numerical simulations of the dynamics of domain walls in the Two-Higgs Doublet Model (2HDM) where the potential has \\(Z_2\\) symmetry in two spatial dimensions. We observed significant differences with the standard case. Although the extreme long-time limit is the same for the \\( 10^5\\) sets of random initial configurations analysed, the percolation process is much slower due to the formation of long-lived loops. We suggest that this is due to the build up of superconducting currents on the walls which could lead ultimately to stationary configurations known as Kinky Vortons. We discuss the relevance of these findings for the production of Vortons in three spatial dimensions.

We present a complete classification of domain wall solutions in the two-Higgs Doublet Model (2HDM) with a global \\(Z_2\\) symmetry, categorised as superconducting, CP-violating, or neither, depending on the scalar particle masses and the ratio of the two Higgs doublets' vacuum expectation values. We demonstrate that any domain wall solution can be reduced to depend on only six of the eight general field components, with further field reductions possible within different regions of the parameter space. Furthermore, we show that the superconducting solutions can be used to construct stable, current-carrying domain walls in two spatial dimensions. Similarly, the CP-violating solutions allow for two-dimensional configurations where CP symmetry is locally broken on the \\(Z_2\\)-symmetric wall, which could provide an out-of-equilibrium environment for CP-violating processes to occur.