Violation of Energy Bounds in Designer Gravity

We continue our study of the stability of designer gravity theories, where one considers antide Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W . It has recently been argued there is a lower bound on the conserved energy in terms of the global minimum of W , if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, there are superpotentials for which these bounds do not hold. ∗UMR 7164 (CNRS, Université Paris 7, CEA, Observatoire de Paris)