Constraining the cosmological evolution of scalar-tensor theories with
  local measurements of the time variation of G
  We determine the conditions for which the constraints from lunar laser
ranging on the time evolution of the local gravitational constant can be
extrapolated to impose constraints on the time evolution of the cosmological
gravitational constant in scalar-tensor theories of modified gravity. We allow
for the possibility that the scalar-tensor theories are non-linear and contain
a screening mechanism. This results in strong constraints on the running of the
cosmological Planck mass described by the Horndeski function
$|\alpha_M|\lesssim 0.002$. We find that our assumptions are valid for most
Vainshtein and kinetic screening models, where the shift symmetry
$\phi\rightarrow\phi + c$ holds, but are violated by some Chameleon and
Symmetron screening models, where the macroscopic equivalence principle is
broken.
