Cosmic Strings and Beyond: From Topological Defects to Gravitational Waves

Cosmic defects are field configurations that are associated with non-vanishing energy but are prevented from decaying into the vacuum by topological or dynamical constraints. They arise naturally during cosmological phase transitions and are a generic product of symmetry-breaking chains in grand unified theories and other extensions of the Standard Model of particle physics. Cosmic defects are of great interest from a theoretical and observational perspective: They contain, on the one hand, plenty of information on the symmetries and the vacuum structure of particle physics theories, while, on the other hand, providing an extremely rich phenomenology. In particular, cosmic strings have gained increased attention as they are expected to produce a stochastic gravitational wave background (GWB) spanning many orders of magnitude in frequency. Such a GWB is attractive as it can be probed by many current and near-future gravitational wave observatories and, at the same time, contains information about the expansion history of the Universe from times when strings were formed until today. In fact, pulsar timing arrays (PTAs), including NANOGrav, have found strong evidence for a GWB. We begin this thesis with a short introduction, providing an overview and motivation for all topics discussed. We begin the first part of this thesis by reviewing the physics of cosmological phase transitions, including a discussion of spontaneous symmetry breaking and high-temperature symmetry restoration, which we use to explain the origin of defects. We will then show in detail how different defects can be classified based on their vacuum topology. This framework can easily be extended to the more complicated metastable defects. Although the symmetry-breaking pattern and the resulting vacuum topology offer insights into the types and basic properties of defects, a complete understanding demands studying their field-theoretical structure. As an original contribution in this regard, we construct explicit field configurations for metastable cosmic strings containing monopoles with partially unconfined flux, providing a basis for future studies of string decay rates. Beyond topological and metastable defects, we comment on a variety of configurations that are stabilised in other ways, such as semilocal or melting defects. In particular, we propose a Standard Model extension that gives rise to plasma-stabilised embedded domain walls. The model is constructed such that electroweak symmetry remains unbroken inside the walls, even after the electroweak phase transition. We show that these walls can drive electroweak baryogenesis and compute the expected baryon-to-entropy ratio from a wall network. This mechanism is, over a wide range of parameters, able to explain the observed baryon asymmetry of the Universe. The second part of this thesis is devoted to cosmic strings and their gravitational wave signatures. We begin by showing that, for cosmological purposes, (local) strings can be effectively described by the Nambu–Goto action. This exploits the fact that the width of strings is typically many orders of magnitude smaller than their curvature radius. We proceed to analyse the properties of solutions to the Nambu–Goto equations of motion, highlighting the origin of microscopic features known as kinks and cusps. Based on this treatment, we introduce the velocity-dependent one-scale (VOS) model to characterise the evolution of long-string networks and show how they can approach a scaling regime through energy loss into string loops. We describe how individual loops lose energy through the emission of gravitational radiation and combine this knowledge with the stochastic properties of the string network to derive the GWB spectrum from decaying loops. As a novel contribution, we will also discuss how the finite string width influences the GWB and at which frequency scales effects are to be expected. Our analysis also uncovers a previously overlooked regime: low-scale cosmic strings. These are characterised by low string tensions and late formation times associated with large initial loop lengths. In contrast to the usually considered high-scale strings, none of the low-scale string loops will have fully decayed by the present time, resulting in a distinctive gravitational wave signature—an oscillating pattern in the GWB close to its peak, exhibiting local minima at integer multiples of the first local minimum. We study in detail the new parameter regime in which low-scale strings arise. We also account for the possibility of loop decay into particle radiation and describe its effect on the loop evolution and the resulting spectra. We find that the features of low-scale-string GWB spectra are largely unaffected by particle decay, but the parameter space from which such strings arise may change drastically. The predicted spectra can, for parts of the parameter space, be probed by future experiments such as BBO and DECIGO. For both low-scale and high-scale cosmic strings, computing the GWB signal is numerically very costly, especially in the case of large parameter scans. Such parameter scans are, however, necessary when evaluating models against observational data. Working with a simplified cosmological expansion history, we obtain fully analytical expressions for the resulting GWB spectra. These results, which represent a central original result of this thesis, are validated against numerical computations across a large region of parameter space. We also provide a detailed discussion of the GWB spectra and present explicit expressions for approximate power-law behaviours and characteristic break frequencies. Our results are valid at all frequencies and cover the entire conceivable range of parameters. Moreover, our computations are able to account for changes in the effective number of relativistic degrees of freedom. Finally, we confront theoretical predictions with observational data from pulsar timing arrays. We use the NANOGrav 15-year data set, which shows evidence for a GWB in the nanohertz frequency range, to find preferred regions of parameter space and place competitive constraints on stable and metastable cosmic strings as well as on cosmic superstrings. In light of the data, we additionally compare all of the cosmic string models to a simplified model for a GWB from inspiraling supermassive black hole binaries. We conclude the thesis with an overview, emphasising the original contributions of this work and pointing towards interesting future research directions.