  We perform cosmological N-body simulations of the Dvali-Gabadadze-Porrati
braneworld model, by solving the full non-linear equations of motion for the
scalar degree of freedom in this model, the brane bending mode. While coupling
universally to matter, the brane-bending mode has self-interactions that become
important as soon as the density field becomes non-linear. These
self-interactions lead to a suppression of the field in high-density
environments, and restore gravity to General Relativity. The code uses a
multi-grid relaxation scheme to solve the non-linear field equation in the
quasi-static approximation. We perform simulations of a flat self-accelerating
DGP model without cosmological constant. The results of the DGP simulations are
compared with standard gravity simulations assuming the same expansion history,
and with DGP simulations using the linearized equation for the brane bending
mode. This allows us to isolate the effects of the non-linear self-couplings of
the field which are noticeable already on quasi-linear scales. We present
results on the matter power spectrum and the halo mass function, and discuss
the behavior of the brane bending mode within cosmological structure formation.
We find that, independently of CMB constraints, the self-accelerating DGP model
is strongly constrained by current weak lensing and cluster abundance
measurements.
