Stability of phantom k-essence theories

We show that phantom dark energy, if it is described by a k-essence theory, has three fundamental problems: first, its Hamiltonian is unbounded from below. Second, classical stability precludes the equation of state from crossing the "Lambda-barrier," w(Lambda)=-1. Finally, both the equation of state and the sound speed are unbounded-the first, from below, the second, from above-if the kinetic term is not bounded by dynamics.