Detecting Fundamental Vector Fields with LISA

The advent of gravitational wave astronomy has seen a huge influx of new predictions for potential discoveries of beyond the Standard Model fields. The coupling of all fundamental fields to gravity, together with its dominance on large scales, makes gravitational physics a rich laboratory to study fundamental physics. This holds especially true for the search for the elusive dark photon, a promising dark matter candidate. The dark photon is predicted to generate instabilities in a rotating black hole spacetime, birthing a macroscopic Bose-Einstein condensate. These condensates can especially form around super massive black holes, modifying the dynamical inspiralling process. This then opens another window to leverage future space-borne gravitational wave antennas to join the hunt for the elusive dark matter particle. This study builds a preliminary model for the gravitational waveform emitted by such a dressed extreme mass-ratio inspiral. Comparing these waveforms to the vacuum scenario allows projections to the potential constrainability on the dark photon mass by space-borne gravitational wave antennas. The superradiant instability of a massive vector field on a Kerr background is calculated and the modification to the dynamics of an inspiralling solar mass-scale compact object is determined with approximations on the backreaction effect of the cloud on the compact object. The end result is the projection that the LISA mission should be able to constrain the dark photon mass using extreme mass ratio inspirals in the range $[1.8 \times 10^{-17}, 4.47 \times 10^{-16}]$ eV.