Extragalactic Proper Motions: Gravitational Waves and Cosmology
  Extragalactic proper motions can reveal a variety of cosmological and local
phenomena over a range of angular scales. These include observer-induced proper
motions, such as the secular aberration drift caused by the solar acceleration
about the Galactic Center and secular extragalactic parallax resulting from our
motion with respect to the cosmic microwave background rest frame. Cosmological
effects include the isotropy of the Hubble expansion, transverse peculiar
velocities induced by large scale structure, the real-time evolution of the
baryon acoustic oscillation, and long-period gravitational waves that deflect
light rays, producing an apparent quadrupolar proper motion pattern on the sky.
We review these effects, their imprints on global correlated extragalactic
proper motions, their expected amplitudes, the current best measurements (if
any), and predictions for Gaia. Finally, we describe key ground- and
space-based observational requirements to measure or constrain these proper
motion signals down to amplitudes of $\sim$0.1 $\mu$as yr$^{-1}$, or $\sim$0.7%
of $H_0$.
