Momentum and Matter Matter for Axion Dark Matter Matters on Earth

We investigate the implications of matter effects to searches for axion Dark Matter on Earth. The finite momentum of axion Dark Matter is crucial to elucidating the effects of Earth on both the axion Dark Matter field value and its gradient. We find that experiments targeting axion couplings compatible with canonical solutions of the strong CP puzzle are likely not affected by Earth's matter effects. However, experiments sensitive to lighter axions with stronger couplings can be significantly affected, with a significant part of the parameter space suffering from a reduced axion field value, and therefore decreased experimental sensitivity. In contrast, the spatial gradient of the axion field can be enhanced along Earth's radial direction, with important implications for ongoing and planned experiments searching for axion Dark Matter.