Null energy condition and superluminal propagation

We study whether a violation of the null energy condition necessarily impliesthe presence of instabilities. We prove that this is the case in a large classof situations, including isotropic solids and fluids relevant for cosmology. Onthe other hand we present several counter-examples of consistent effectivefield theories possessing a stable background where the null energy conditionis violated. Two necessary features of these counter-examples are the lack ofisotropy of the background and the presence of superluminal modes. We arguethat many of the properties of massive gravity can be understood by associatingit to a solid at the edge of violating the null energy condition. We brieflyanalyze the difficulties of mimicking $\dot H>0$ in scalar tensor theories ofgravity.Comment: 46 pages, 6 figure