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 λ_{DGP}. We show that this theory has strong interactions at a length scale λ_3 ~ (λ_{DGP}^2 / M_P)^{1/3}. If λ_{DGP} is of order the Hubble length, then the theory loses predictivity at distances shorter than λ_3 ~ 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 λ_3. Finally, we examine the dynamics of the longitudinal Goldstone mode when the background geometry is curved.

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