Compact objects in and beyond the Standard Model

Compact objects are unique probes of the strong gravity regime and may be the key to understanding long-standing puzzles in fundamental physics. These include the nature of dark matter, the possible extension of Einstein's gravity, and the fate of spacetime singularities. The advent of gravitational-wave astronomy provides new observations with present and future interferometers and is a great opportunity to address such foundational issues. We consider a theory in which a real scalar field is Yukawa-coupled to a fermion and has a potential with two non-degenerate vacua. If the coupling is sufficiently strong, a collection of N fermions deforms the true vacuum state, creating energetically-favored false-vacuum pockets in which fermions are trapped. We embed this model within General Relativity and prove that it admits self-gravitating compact objects where the scalar field acquires a non-trivial profile due to non-perturbative effects. We discuss some applications of this general mechanism in and beyond the Standard Model. Finally, we provide distinctive signatures of the model in the gravitational wave signal using tidal Love numbers, offering a way to distinguish these solutions from other types of compact objects.