Simulating the quartic Galileon gravity model on adaptively refined meshes

We develop a numerical algorithm to solve the high-order nonlinear derivativecoupling equation associated with the quartic Galileon model, and implement it in a modied version of the ramses N-body code to study the eect of the Galileon field on the largescale 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 t 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 eld 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 modied gravity theories and the importance of performing self-consistent N-body simulations for these theories.