Lattice Simulations of Domain Wall Networks in the Scaling Regime and Implications for Dark Matter

While gravitational evidence firmly establishes Dark Matter (DM) as a dominant component of the universe's matter budget, its fundamental nature and production mechanisms remain an open puzzle. Alongside standard thermal freeze-out candidates, non-thermal production via topological defects offers a compelling theoretical alternative. This thesis investigates the cosmological evolution and subsequent DM genesis from metastable Domain Walls (DWs), topological structures that could form as a result of Spontaneous Symmetry Breaking (SSB) in the early universe. While the initial chapters review the lines of evidence for DM, its potential production mechanisms, and the theoretical foundation of DWs, the core of this work focuses on performing 3D lattice field simulations of DW networks. These simulations are conducted using the CosmoLattice package within an expanding, radiation-dominated background. The study explores two distinct theoretical frameworks: an axion field with a periodic potential, and a generic real scalar field model weakly coupled to the Standard Model via a Higgs portal. In both scenarios, perfectly stable DWs would lead to a cosmological catastrophe by overclosing the universe. To resolve this, we implement a symmetry-breaking bias in the scalar potentials that lifts the vacuum degeneracy, subjecting the DW network to a pressure term that forces its eventual collapse and the radiation of stable particles. A major focus of this research is the detailed dynamical and spectral analysis of the decaying network. By tracking the evolution of the fields on the lattice, we observe the network reaching the attractor "scaling regime", where the DW area per horizon volume becomes constant. During and after this phase, we investigate the specific physical mechanisms responsible for the network's energy loss. Building upon recent theoretical models and numerical studies, we analyze complex dynamical processes such as the flattening of DW surface fluctuations, the self-chopping of the walls, and the rapid contraction and collapse of horizon-sized compact DWs. By filtering out the DW contributions to extract the free particle spectrum, we identify distinct kinetic energy regimes associated with these processes, finally predicting the total DM relic density produced by the annihilating DWs for both models. This approach allows us to map the viable theoretical parameter space, specifically constraining the energy bias and evaluating it against stringent cosmological bounds.