DBI and the Galileon reunited

We derive the relativistic generalization of the Galileon, by studying the brane position modulus of a relativistic probe brane embedded in a five- dimensional bulk. In the appropriate Galilean contraction limit, we recover the complete Galileon generalization of the DGP decoupling theory and its conformal extension. All higher order interactions for the Galileon and its relativistic generalization naturally follow from the brane tension, induced curvature, and the Gibbons-Hawking-York boundary terms associated with all bulk Lovelock invariants. Our approach makes the coupling to gravity straightforward, in particular allowing a simple rederivation of the nonmini- mal couplings required by the Covariant Galileon. The connection with the Lovelock invariants makes the well-defined Cauchy problem manifest, and gives a natural unification of four dimensional effective field theories of the DBI type and the Galileon type.