Astrometric Search for Ultralight Dark Matter

Precision astrometry offers a way to probe new physics. By measuring the angular position of light sources at unprecedented precision, astrometry could probe minuscule fluctuations of underlying spacetime. This work explores the possibility of probing ultralight dark matter candidates using precision astrometry. Through the coherent and stochastic density fluctuations over the scale of its wavelength, ultralight dark matter perturbs the propagation of light and the geodesics of the observer and source, leading to unique time-dependent signatures in the angular position of background light sources. With detector specifications similar to the current and future astrometry observations, such as Gaia and Roman Space Telescope, it is shown that the ultralight scalar dark matter of mass $10^{-18}\,{\rm eV} \, \textrm{--} \, 10^{-16} \,{\rm eV}$ could be probed when its density near the solar system is about a few thousand times larger than the nominal dark matter density measured on a much larger kpc-scale. This sensitivity is comparable to current pulsar timing array observations at a similar mass range. Explicit expressions for the angular deflection induced by most generic metric perturbations are derived and its gauge invariance is explicitly checked at the linear order.