Probing new physics with exotic compact objects: the role of fermion soliton stars

Many of the biggest puzzles in physics, such as the nature of dark matter and the behavior of spacetime singularities, stem from the interplay between gravity and quantum mechanics. Compact objects, like neutron stars and black holes, offer a unique setting to investigate these questions, as they probe strong gravitational fields and may be the only possible way to observe dark particles. With the recent discovery of gravitational waves, we now have an uncharted way to study such extreme environments, potentially shedding light on those fundamental issues. This thesis focuses on fermion soliton stars, a class of compact objects that emerge from a theory in which a nonlinear self-interacting scalar field couples with fermions via a Yukawa interaction, resulting in an effective fermion mass that depends on the fluid properties. We elucidate the fundamental features of this model and its links to the Standard Model and beyond. Moreover, we provide distinctive signatures of the model in the gravitational wave signal, offering a way to distinguish fermion soliton stars from other types of compact objects.