The QCD axion and axion-like particles are compelling dark matter candidates and can solve the strong CP problem. In this talk, I will demonstrate how fundamental properties of QCD axions, such as their potential, depend on finite density and temperature.

The presence of a finite density background, such as found in stars and planets, reduces the axion mass and can even dominate the vacuum mass in large parts of the parameter space. In such a scenario, the axion field is displaced from its zero-density minimum, allowing a non-trivial field configuration to form that interpolates between the two minima in space. This has interesting phenomenological implications. For instance, the presence of such a non-trivial axion field profile can be tested with white dwarf - neutron star or neutron star - neutron star inspirals.

Additionally, there can be a significant backreaction on the compact object under consideration. As I will show, displaced…