Spatial variation of fundamental couplings and Lunar Laser Ranging
  If the fundamental constants of nature have a cosmic spatial variation, there
will in general be extra forces with a preferred direction in space which
violate the equivalence principle. We show that the millimeter-precision Apache
Point Observatory Lunar Laser-ranging Operation provides a very sensitive probe
of such variation that has the capability of detecting a cosmic gradient of the
ratio between the quark masses and the strong interaction scale at the level
with the gradient of ln (m_quark/Lambda_QCD) ~ 2.6 x 10^-6 Glyr^-1, which is
comparable to the cosmic gradients suggested by the recently reported
measurements of Webb et al. We also point out the capability of presently
planned improved equivalence principle tests, at the Delta g/g < 10^-17 level,
to probe similar cosmic gradients.
