Covariant Galileon and a consistent self-accelerating universe

In this paper we show that the flat-space Galilean theories with up to three scalars in the equation of motion (the quartic Galileons) are recovered in the decoupling limit of certain scalar theories non-minimally coupled to gravity, the so-called "Slotheonic" theories. These theories are also invariant under the generalized Galilean shifts in curved spacetime. While Galilean self-(derivative) couplings are not explicit in the action, they appear after integrating out gravity. We then argue that Galilean super-symmetric theories may only be found in the context of supergravity. Finally, we discuss the possibility that Slotheonic theories are the effective four-dimensional theories of consistent Dvali-Gabadadze-Porrati-like models with self- accelerating cosmological solutions. Moreover, we show that the quartic and cubic Galileons in consistent Dvali-Gabadadze-Porrati models cannot be decoupled.