Spherical collapse and the halo model in braneworld gravity

We present a detailed study of the collapse of a spherical perturbation in Dvali-Gabadadze-Porrati (DGP) braneworld gravity for the purpose of modeling simulation results for the halo mass function, bias, and matter power spectrum. The presence of evolving modifications to the gravitational force in the form of the scalar brane-bending mode leads to qualitative differences to the collapse in ordinary gravity. In particular, differences in the energetics of the collapse necessitate a new, generalized method for defining the virial radius which does not rely on strict energy conservation. These differences and techniques apply to smooth dark energy models with w not equal -1 as well. We also discuss the impact of the exterior of the perturbation on collapse quantities due to the lack of a Birkhoff theorem in DGP. The resulting predictions for the mass function, halo bias, and power spectrum are in good overall agreement with DGP N-body simulations on both the self-accelerating and normal branch. In particular, the impact of the Vainshtein mechanism as measured in the full simulations is matched well. The model and techniques introduced here can serve as practical tools for placing consistent constraints on braneworld models using observations of large-scale structure.