Exploring Vainshtein mechanism on adaptively refined meshes

There has been a lot of research interest in modified gravity theories which utilise the Vainshtein mechanism to recover standard general relativity in regions with high matter density, such as the Dvali-Gabadadze-Porrati and Galileon models. The strong nonlinearity in the field equations of these theories implies that accurate theoretical predictions could only be made using high-resolution cosmological simulations. Previously, such simulations were usually done on regular meshes, which limits both their performance and the accuracy. In this paper, we report the development of a new algorithm and code, based on ECOSMOG, that uses adaptive mesh refinements to improve the efficiency and precision in simulating the models with Vainshtein mechanism. We have made various code tests against the numerical reliability, and found consistency with previous simulations. We also studied the velocity field in the self-accelerating branch of the DGP model. The code, parallelised using MPI, is suitable for large cosmological simulations of Galileon-type modified gravity theories.