The null energy condition and cosmology

Field theories that violate the null energy condition {(}NEC{\rm)} are of interest both for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w<-1$. We consider two recently proposed models that violate the NEC. The ghost condensate model requires higher-derivative terms in the action, and this leads to a heavy ghost field and energy unbounded from below. We estimate the rates of particle decay and discuss possible mass limitations to protect the stability of matter in the ghost condensate model. The nonlocal stringy model that arises from a cubic string field theory and exhibits a phantom behavior also leads to energy unbounded from below. In this case, the energy spectrum is continuous, and there are no particle-like excitations. This model admits a natural UV completion because it comes from superstring theory.