Analytic Description of DGP Perturbations on All Scales

Abstract

We develop analytic solutions for the linear evolution of metric perturbations in the DGP braneworld modified gravity scenario including near-horizon and superhorizon modes where solutions in the bulk are required. These solutions apply to both the self-accelerating and normal branch and elucidate the nature of coordinate singularities and initial data in the bulk as well as their effect on perturbation evolution on the brane. Even on superhorizon scales, the evolution of metric perturbations is no longer necessarily scale free due to multiple resonances in the bulk. Based on these analytic solutions, we devise convenient fitting functions for the evolution that bridge the various spatial and temporal regimes. Compared with a direct numerical integration of the bulk equations, the fits are accurate at the percent level and are sufficient for current and upcoming observational tests.