Boundary Terms and Junction Conditions for Generalized Scalar-Tensor   Theories
  We compute the boundary terms and junction conditions for Horndeski's panoptic class of scalar-tensor theories, and write the bulk and boundary equations of motion in explicitly second order form. We consider a number of special subclasses, including galileon theories, and present the corresponding formulae. Our analysis opens up of the possibility of studying tunnelling between vacua in generalized scalar-tensor theories, and braneworld dynamics. The latter follows because our results are independent of spacetime dimension. 
Antonio Padilla and Vishagan Sivanesan
gr-qc hep-th