Future dark energy constraints from measurements of quasar parallax: Gaia, SIM and beyond

(Abridged) A consequence of the Earth's motion with respect to the CMB is that over a 10 year period it will travel a distance of ~800 AU. As first noted by Kardashev in 1986, this baseline can be used to carry out astrometric measurements of quasar parallaxes, so that only microarcsecond precision is necessary to detect parallax shifts of objects at gigaparsec distances. Such precision will soon be approached with the launch of the astrometric satellites Gaia and SIM. We use a Fisher matrix formalism to investigate the constraints that these and future missions may be able to place on the cosmological distance scale and dark energy. We find that by observing around a million quasars as planned, an extended 10 year Gaia mission could detect quasar parallax shifts at the 2.8 sigma level and so measure the Hubble constant to within 25 km/s. For the interferometer SIMLite, a Key Project using 2.4 % of the total mission time to observe 750 quasars could detect the effect at the 2 sigma level. Gaia and a dedicated SIMLite only weakly constrain the presence of a cosmological constant at the ~1 sigma levels. We also investigate future mission concepts, such as an interferometer similar in scope and design to NASA's Terrestrial Planet Finder. This could in principle measure the dark energy parameters w_0 and w_a with high precision, yielding a Figure of Merit larger than the stage IV experiments considered by the the Dark Energy Task Force. Unlike perhaps all other probes of dark energy there appear to be no obvious astrophysical sources of systematic error. There is however uncertainty regarding the statistical errors. As well as measurement error, there will be small additional contributions from image centroiding of variable sources, quasar peculiar motions and weak microlensing by stars along the line of sight.