Simulating the quartic Galileon gravity model on adaptively refined
  meshes
  We develop a numerical algorithm to solve the high-order nonlinear
derivative-coupling equation associated with the quartic Galileon model, and
implement it in a modified version of the RAMSES N-body code to study the
effect of the Galileon field on the large-scale matter clustering. The
algorithm is tested for several matter field configurations with different
symmetries, and works very well. This enables us to perform the first
simulations for a quartic Galileon model which provides a good fit to the
cosmic microwave background (CMB) anisotropy, supernovae and baryonic acoustic
oscillations (BAO) data. Our result shows that the Vainshtein mechanism in this
model is very efficient in suppressing the spatial variations of the scalar
field. However, the time variation of the effective Newtonian constant caused
by the curvature coupling of the Galileon field cannot be suppressed by the
Vainshtein mechanism. This leads to a significant weakening of the strength of
gravity in high-density regions at late times, and therefore a weaker matter
clustering on small scales. We also find that without the Vainshtein mechanism
the model would have behaved in a completely different way, which shows the
crucial role played by nonlinearities in modified gravity theories and the
importance of performing self-consistent N-body simulations for these theories.
