On the Null Energy Condition and Cosmology
  Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of cosmological dark energy with the equation of state parameter $w<-1$. We discuss the consistency of two recently proposed models that violate the NEC. The ghost condensate model requires higher-order derivative terms in the action. It leads to a heavy ghost field and unbounded energy. We estimate the rates of particles decay and discuss possible mass limitations to protect 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 unbounded energy. In this case the spectrum of energy is continuous and there are no particle like excitations. This model admits a natural UV completion since it comes from superstring theory. 
I. Ya. Aref'eva and I.V. Volovich