Composite Axion Models and Q-Ball Superradiance

The Standard Model is the most successful theory in physics, yet it leaves key questions open. One question is the strong CP problem: the strong interaction conserves parity and time reversal to better than $10^{-10}$, a smallness that finds no explanation within the Standard Model. The Peccei--Quinn mechanism resolves this dynamically through a Goldstone boson called the axion; however, a realistic axion model must overcome the hierarchy problem of the Peccei--Quinn scale, the axion quality problem, and the cosmological domain-wall problem, while the heavy relics predicted by such models must not overclose the universe. Other questions such as dark matter and the baryon asymmetry also require solutions beyond the Standard Model. Some extensions of the Standard Model that attempt to address dark matter or the baryon asymmetry have rich scalar sectors that can generically support non-topological solitons. These solitons exchange charge and energy with their surrounding environment, so understanding their interaction is essential. This thesis takes up these two topics separately. In the first part of this thesis, we construct explicit composite axion models, in which the Peccei--Quinn scale arises from a new confining interaction rather than an elementary scalar. We derive a general greatest-common-divisor criterion for computing the domain-wall number, and then construct two models with domain-wall number one in which the string-wall network self-annihilates: a deconstructed pair of chiral $SU(5)$ sectors, whose assumed confinement pattern we critically examine, and two vector-like sectors sharing a gauged Abelian symmetry (an anomaly-free direction orthogonal to the anomalous Peccei--Quinn direction). The leading operators that can explicitly break the Peccei--Quinn symmetry of both models appear at dimension nine, high enough to leave the strong CP solution intact. Both models predict stable colored relics, so we study the phenomenology of a short secondary inflationary epoch that can dilute them, leaving viable parameter space in which the string network re-enters the horizon near the QCD transition. This re-entry timing preserves the standard post-inflationary axion cosmology.\\ The second part of this thesis is independent of the first, and it concerns superradiant scattering from Q-balls; in particular, it determines when linear scattering theory can be trusted. The charge and energy transferred to the Q-ball are fixed by unitarity in terms of a single particle--antiparticle conversion probability, and we show that the energy transferred coincides exactly with the energy cost $\mu Q$ of the transferred charge. Nonlinear lattice simulations confirm the linear description for incident amplitudes below $\sim 10^{-2}$ of the soliton wall value. We also extend the linear formalism to the two-field Friedberg--Lee--Sirlin soliton, where the additional neutral field opens further conversion channels. Together, these studies provide composite axion models that remain viable in a post-inflationary cosmology, and a quantitative amplitude threshold below which perturbative treatments of soliton scattering can be trusted.