  We study quasi-static perturbations in a cosmological background in the
Dvali-Gabadadze-Porrati (DGP) braneworld model. We identify the Vainshtein
radius at which the non-linear interactions of the brane bending mode become
important in a cosmological background. The Vainshtein radius in the early
universe is much smaller than the one in the Minkowski background, but in a
self-accelerating universe it is the same as the Minkowski background. Our
result shows that the perturbative approach is applicable beyond the Vainshtein
radius for weak gravity by taking into account the second order effects of the
brane bending mode. The linearised cosmological perturbations are shown to be
smoothly matched to the solutions inside the Vainshtein radius. We emphasize
the importance of imposing a regularity condition in the bulk by solving the 5D
perturbations and we highlight the problem of ad hoc assumptions on the bulk
gravity that lead to different conclusions.
