Testing Modified Gravity Theories via Wide Binaries and GAIA
  The standard LambdaCDM model based on General Relativity (GR) including cold
dark matter (CDM) is very successful at fitting cosmological observations, but
recent non-detections of candidate dark matter (DM) particles mean that various
modified-gravity theories remain of significant interest. The latter generally
involve modifications to GR below a critical acceleration scale $\sim 10^{-10}
\, m \, s^{-2}$. Wide-binary (WB) star systems with separations $> 5 \, kAU$
provide an interesting test for modified gravity, due to being in or near the
low-acceleration regime and presumably containing negligible DM. Here, we
explore the prospects for new observations pending from the GAIA spacecraft to
provide tests of GR against MOND or TeVes-like theories in a regime only
partially explored to date. In particular, we find that a histogram of (3D)
binary relative velocities against circular velocity predicted from the (2D)
projected separations predicts a rather sharp feature in this distribution for
standard gravity, with an 80th (90th) percentile value close to 1.025 (1.14)
with rather weak dependence on the eccentricity distribution. However,
MOND/TeVeS theories produce a shifted distribution, with a significant increase
in these upper percentiles. In MOND-like theories {\em without} an external
field effect, there are large shifts of order unity. With the external field
effect included, the shifts are considerably reduced to $\sim 0.04 - 0.08$, but
are still potentially detectable statistically given reasonably large samples
and good control of contaminants. In principle, followup of GAIA-selected wide
binaries with ground-based radial velocities accurate to < 0.03 km/s should be
able to produce an interesting new constraint on modified-gravity theories.
