Cosmology and Astrophysics of CP-Violating Axions

We study the cosmology and astrophysics of axion-like particles (ALPs) with CP-violating Yukawa couplings to nucleons. At finite nucleon density, the ALP's dynamics is governed by an effective potential which is the sum of the bare periodic potential and a linear potential whose strength depends on the nucleon density. We identify a critical nucleon density $\rho_c$ controlling the dynamics. At densities smaller than $\rho_c$ the effective potential is a tilted sinusoidal curve and the field is displaced from its zero-density minimum. At densities larger than $\rho_c$ the minima (and maxima) are absent, and the ALP is destabilized. Astrophysically, this implies that neutron stars can source a radial ALP field, providing a complementary probe to equivalence principle tests. Cosmologically, the ALP may have been destabilized in the early Universe and could have made large field excursions. We discuss model-building applications of our results for such early universe scenarios.