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Cosmic strings are topological defects expected to emerge in various cosmological scenarios, as the temperature of the Universe decreases and it undergoes a sequence of symmetrybreaking phase transitions. Although these objects have not yet been observed—either directly or indirectly—their detection would provide valuable insight into the high-energy physics that shaped the early Universe. Conversely, ruling them out would require a substantial revision of our current understanding of these fundamental processes.
In the effort to search for cosmic string signatures, robust theoretical models are essential for interpreting observational data. While such models may arise from field theory and numerical simulations, they face significant challenges. One major difficulty stems from the vast range of length and time scales involved in the evolution of cosmic strings, making full numerical treatment extremely demanding. As a result, phenomenological models have been developed to capture the macroscopic behavior of string networks. Among these, the Velocity dependent One-Scale model (VOS) model stands out for treating the network as a thermodynamic system, characterizing its key properties and predicting its large-scale evolution.
Extensions of this framework account for superconducting cosmic strings, which carry internal currents and possess additional degrees of freedom. These are well described by the Charge-Velocity dependent One-Scale model (CVOS), a generalization of the VOS formalism. A central feature of both models is loop formation, which acts as the primary energy loss mechanism of the network.
In this dissertation, we first aimed to understand how superconducting loops evolve under various conditions, considering different expansion rates and physical models. We analyzed the role played by the internal charge and current in shaping their dynamics. Later, we propose a novel mechanism that, in principle, allows the cosmic string network to gain energy. We consider current-carrying cosmic strings subjected to an external magnetic field, and investigate how this interaction influences the evolution of the network. We develop a mathematical formalism extending the CVOS model and analyze its late-time stable solutions. These solutions aim to describe the large-scale behavior of the string network while simultaneously placing constraints on the properties of the ambient magnetic field.