Gravitational couplings in Chameleon models
  We consider cosmological models where dark energy is described by a dynamical
field equipped with the Chameleon screening mechanism, which serves to hide its
effects in local dense regions and to conform to Solar System observations. In
these models, there is no universal gravitational coupling and here we study
the effective couplings that determine the force between massive objects,
$G_N$, and the propagation of gravitational waves, $G_{gw}$. In particular, we
revisit the Chameleon screening mechanism without neglecting the time
dependence of the galactic environment where local regions are embedded in, and
analyze the induced time evolution on $G_N$ and $G_{gw}$, which can be tested
with Lunar Laser Ranging and direct gravitational waves observations. We
explicitly show how and why these two couplings generically differ. We also
find that due to the particular way the Chameleon screening mechanism works,
their time evolutions are highly suppressed in the weak-field non-relativistic
approximation.
