Searching for ultralight dark matter through frequency modulation of gravitational waves

Ultralight bosons, naturally appearing in well-motivated extensions to the Standard Model, can constitute all the dark matter. Models with particle mass close to the smallest phenomenologically allowed exhibit coherent field configurations at (sub)galactic scales, oscillating at a frequency corresponding to the fundamental mass of the dark matter particle. The gravitational field of these structures inherits the dark matter field's coherent oscillations, leaving an imprint on gravitational (and electromagnetic) waves sourced close to (or in) such overdensities. This happens via a heterodyning frequency modulation, which can later be decoded in a gravitational-wave detector. An analogous effect occurs in models with universal (conformal) couplings of ultralight bosons with ordinary matter, generated by the direct interaction with the oscillating field. In this work, we explore this phenomenon in detail and assess the capability of near-future interferometers to probe ultralight dark matter and its potential conformal couplings to matter. Using astrophysical population models, together with results from cosmological simulations, we find that the observation of gravitational waves from spinning neutron stars at the Galactic Center with the Einstein Telescope/Cosmic Explorer would be particularly effective in constraining ultralight dark matter.