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 lambda(DGP). We show that this theory has strong interactions at a length scale lambda(3) similar to (lambda(DGP)(2)/M-P)(1/3). If lambda(DGP) is of order the Hubble length, then the theory loses predictivity at distances shorter than lambda(3) similar to 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 lambda(3). Finally, we examine the dynamics of the longitudinal Goldstone mode when the background geometry is curved.