Strong interactions and stability in the DGP model

The model of Dvali, Gabadadze, and Porrati (DGP) gives a simple geometrical setup in which gravity becomes 5-dimensional at distances larger than a length scale λDGP. We show that this theory has strong interactions at a length scale λ₃ ∼ (λ_DGP²/Mp) ^1/3. If λ_DGP is of order the Hubble length, then the theory loses predictivity at distances shorter than λ₃ ∼ 1000 km. The strong interaction can be viewed as arising from a longitudinal 'eaten Goldstone' mode that gets a small kinetic term only from mixing with transverse graviton polarizations, analogous to the case of massive gravity. We also present a negative-energy classical solution, which can be avoided by cutting off the theory at the same scale scale λ₃. Finally, we examine the dynamics of the longitudinal Goldstone mode when the background geometry is curved.