Probing Axion Dark Matter with Electric Dipole Moments

Electric dipole moments (EDMs) of fundamental particles are among the most sensitive probes of physics beyond the Standard Model, with current experiments setting extremely stringent upper bounds. This thesis investigates the potential of EDM searches to probe axion dark matter, focusing on how the oscillatory nature of the dark matter field can induce time-dependent CP-violating effects. Special attention is given to the case of derivative axion couplings, which naturally arise in the Peccei-Quinn solution to the strong-CP problem. We critically examine recent proposals for an axion-induced oscillating electron EDM (eEDM), clarifying the theoretical consistency of such effects. An independent analysis based on the electron propagator in an axion background confirms that, in the shift-symmetric (derivative) basis, the eEDM vanishes in the massless axion limit, as required by axion shift invariance. The same conclusion follows in the pseudoscalar basis after an appropriate chiral rotation, in accordance with the equivalence theorem. Finally, we review the impact of axion dark matter backgrounds on atomic EDMs, emphasizing that present experimental sensitivities are insufficient to detect the expected oscillations.