Generalized Galileon Model -- cosmological reconstruction and the   Vainshtein mechanism --
  Explicit formulae of the equations in the generalized Galileon models are given. We also develop the formulation of the reconstruction. By using the formulation, we can explicitly construct an action which reproduces an arbitrary development of the expansion of the universe. The conditions how the reconstructed solution becomes stable and therefore it becomes an attractor solution are also given. Working in the static and spherically symmetric space-time, we investigate how the Vainshtein mechanism works in the generalized Galileon model and the correction to the Newton law becomes small. It is also shown that any spherically symmetric and static geometry can be realized by properly choosing the form of the action, which may tell that the solution could have fourth hair corresponding to the scalar field. 
Norihito Shirai, Kazuharu Bamba, Shota Kumekawa, Jiro Matsumoto,   Shin'ichi Nojiri
hep-th astro-ph.CO gr-qc