Localized gravity and higher curvature terms

We consider localization of gravity in smooth domain wall solutions of gravity coupled to a scalar field with a generic potential in the presence of the Gauss–Bonnet term. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. We point out that the presence of the Gauss–Bonnet term does not allow flat solutions with localized gravity that violate the weak energy condition. We also point out that in the presence of the Gauss–Bonnet term infinite tension flat domain walls violate positivity. In fact, for flat solutions unitarity requires that on the solution the scalar potential be bounded below.