The search for new physics beyond the Standard Model (BSM) is driven by deep theoretical puzzles, including the strong CP problem, the nature of dark matter, and the origin of the matter-antimatter asymmetry. I will begin by describing my work on heavy axion models, which offer a solution to the strong CP problem while predicting collider-visible axions. These models also undergo confining phase transitions that leave imprints in the form of stochastic gravitational wave backgrounds. The interplay between the symmetries of the high energy and the masses of Goldstone bosons in the confined phase enables the estimation of this signal, providing a window across the barrier of strong coupling.
This connection between symmetries, strong dynamics, and cosmological signals inspired new avenues in my pursuit of BSM physics. I will discuss how gravitational wave signals can serve as a complementary probe to shed light on which effective field theory captures the nature of electroweak symmetry breaking. I will then discuss how phase transitions influence dark matter and baryogenesis, motivating new models to address these questions. Finally, my interest in strong coupling has led to work on a systematic effective theory for Hamiltonian truncation, culminating in a new next-to-leading order result that establishes the reliability of this tool for probing nonperturbative physics.