Chameleon Field in a Spherical Shell System
  We investigate the validity of screening mechanism of the fifth force for
chameleon field in highly inhomogeneous density profile. For simplicity, we
consider a static and spherically symmetric system which is composed of
concentric infinitely thin shells. We calculate the fifth force profile by
using a numerical method for a relatively large Compton wavelength of the
chameleon field. An approximate solution is also derived for the small Compton
wavelength limit. Our results show that, if the thin-shell condition for the
corresponding smoothed density profile is satisfied, the fifth force is safely
screened outside the system irrespective of the configuration of the shells
inside the system. In contrast to the screening outside the system, we find
that the fifth force can be comparable to the Newtonian gravitational force
inside the system. If the system is highly inhomogeneous, the chameleon field
cannot trace the potential minimum varying with the density and repeats being
kicked, climbing up and rolling down the potential even when the effective mass
of the chameleon field is sufficiently large in the system on average. One
should not feel complacent about the wellbehavedness of the fifth force field
with an averaged density distribution when we consider inhomogeneous objects.
