We use $N$-body simulations to study the nonlinear structure formation in brane-induced gravity, developing a new method that requires alternate use of Fast Fourier Transforms and relaxation. This enables us to compute the nonlinear matter power spectrum and bispectrum, the halo mass function, and the halo bias. From the simulation results, we confirm the expectations based on analytic arguments that the Vainshtein mechanism does operate as anticipated, with the density power spectrum approaching that of standard gravity within a modified background evolution in the nonlinear regime. The transition is very broad and there is no well defined Vainshtein scale, but roughly this corresponds to $k_{*}\simeq 2h{\mathrm{Mpc}}^{-1}$ at redshift $z=1$ and $k_{*}\simeq 1h{\mathrm{Mpc}}^{-1}$ at $z=0$. We checked that while extrinsic curvature fluctuations go nonlinear, and the dynamics of the brane-bending mode $C$ receives important nonlinear corrections, this mode does get suppressed compared to density perturbations, effectively decoupling from the standard gravity sector. At the same time, there is no violation of the weak field limit for metric perturbations associated with $C$. We find good agreement between our measurements and the predictions for the nonlinear power spectrum presented in paper I, that rely on a renormalization of the linear spectrum due to nonlinearities in the modified gravity sector. A similar prediction for the mass function shows the right trends. Our simulations also confirm the induced change in the bispectrum configuration dependence predicted in paper I.

• Received 20 July 2009

DOI:https://doi.org/10.1103/PhysRevD.80.104005