Near-horizon solution for Dvali-Gabadadze-Porrati perturbations

We develop a scaling ansatz for the master equation in Dvali, Gabadadze, Porrati cosmologies, which allows us to solve the equations of motion for perturbations off the brane during periods when the on-brane evolution is scale free. This allows us to understand the behavior of the gravitational potentials outside the horizon at high redshifts and close to the horizon today. We confirm that the results of Koyama and Maartens are valid at scales relevant for observations such as galaxy-ISW correlations. At larger scales, there is an additional suppression of the potential which reduces the growth rate even further and would strengthen the integrated Sachs-Wolf effect.