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

A consequence of the Earth's well-measured motion with respect to the cosmic microwave background is that over a 10-yr period it will travel a distance of similar to 800 au. As first pointed out by Kardashev in 1986, this distance can be used as a baseline 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 Space Interferometry Mission (SIM). We use a Fisher matrix formalism to investigate the constraints that these and future, even more ambitious, missions may be able to place on the cosmological distance scale and the parameters describing dark energy. We find that by observing around a million quasars as planned, an extended 10 yr Gaia mission should have the capability to detect quasar parallax shifts at the 2.8 sigma level and so measure the Hubble constant to within 25 km s(-1). For the interferometer SIM (in its currently proposed SIMLite configuration) a Key Project using 2.4 per cent of the total mission time to observe 750 quasars could detect the effect at the 2 sigma level and dedicated use of the instrument at the 3.3 sigma level. In a concordance cosmological model, Gaia and dedicated SIMLite only weakly constrain the presence of a cosmological constant at the similar to 1 sigma levels. We also investigate a range of 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 precision sigma(w0) = 0.02 and sigma(wa) = 0.05, respectively, yielding a Figure of Merit larger than the stage IV experiments considered in the report of the Dark Energy Task Force. Unlike perhaps all other probes of dark energy there appear to be no obvious astrophysical sources of systematic error on these measurements. 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.